Exploring The Optimistic Virtual Machine by Ben Jones, Karl Floersch (Devcon5)

[Applause] but it doesn't matter because I've waited for many minutes okay so we're talking about later today I look like about particularly something which is difficult the obligatory machine now when most people think of a virtual machine they think of stacks and registers and all these other things and I got a incredibly advanced computer scientist so I think I can make an argument that this thing's a virtual machine but usually when I say oh yeah I'm can we do something else so actually we're gonna be talking about today is one particular subset called optimistic semantics and basically the idea is what's going on with this layer two and how can we try to bring it under your sort of more unified I'm well what's up guys we're unified umbrella okay so what are we gonna talk about today first thing we're gonna do is we're gonna spend some time bisecting what layer two is today and sort of looking at how it functions and what are the conversation the next thing we're going to do is we are going to take all the components that we use in trying to describe layer two and talk about how we should try to use those to build the layer two okay and the last thing here which pema this is really an agenda point but it's something that i want is i do not know how to finish these slides okay so the reason that this is like not a video that is on our website or being posted on our twitter is because of you guys this means is that there's no point in us having this here unless people ask questions and engage okay so before I go forward I'm not going to say no word until I ask the question do you feel like perfect you optimistic about like audience participation [Music] to optimistic is like supply okay great okay I let so let's gonna make this a little bit so we have a later - later - is popping you could even say it's a any brilliant explosion okay it's under the sex building I think to quote me about my really big plan do very very simple payment channels a bitcoin then we have a lightning power come out in 2015 then we started seeing more different state channels design sprites virtual channels generalize channels right we start because a true bit that I and I come from a background of plasma and plasma is perhaps the most exciting but also guilty printing huge amounts of diverse designs and varying implementations this is a place small selection of the code plasma flavors that we have in the classroom design world I mean even worse I'll be company you other incredible things happening we've got roll-ups the optimistic flavor and the CK flavor no cuz it's a commit chain which is basically possible that is why cultures possibly because they're not plasma our maturity was in the room with another better version of two of it right there's lots and lots of exams use coming about right so this is wonderful as a research in this very exciting as a user who wants we didn't get the big simulator to this is very exciting but it's not like all of these ideas are totally unique right at the end of the day most step or I'll go all around one thing and that is this notion of disputes right usually something happens on the off main chain and then someone claims something happen on the main chain and then someone else disputes them about it right sort of the basis based things that happens and what we see a lot of papers completely reinvent this real right so these are you know layer 2 protocol admin and layer 2 protocol head plus one this is like often sort of you know what we get in this ingest of course you know citations are very important and everyone's standing on the shoulders of giants but everything uses disputes this is the point ok I think I realized is that the sort of meme of one helps you can rule them all up and out outside view the Bitcoin world because unfortunately only lightning is really possible on Bitcoin this is a lie this is just a plain line ok what we see is the different layer two designs are built for different applications they're built for different use cases so what we need to say see is not one l2 the global but like you know sand well Jesus shaking hands and interoperating because the reality users are going to want you some many such applications the layers you can provide but it's not going to be just one that gives it to them that's not to say that we're gonna have you know thousands perhaps but it was probably on more than one ok so I have not any questions now something's composite off and they've got the questions cuz I would agree with this ain't hot tanks then gonna prove me wrong there's only one L to rule them all concert in all to death no okay good that's what I do here so let's try to understand a bit about what layer to really is okay so like in a high-level I think there's like four pretty distinct things that go into layer two okay four steps if you were so the one thing that you do is you check the blockchain see where DEFCON so I'll say three check the blockades to state see what's going on right now right the next thing that you do and this is the sort of layer apart the second layer is you get some local information and you look at it observe it right the third thing that you do is you make some kind of an assumption right so this is usually of the form I will dispute things and we'll be talking about that a lot here but there's lots of different assumptions you can name then the last thing you do is you make some prediction about future l2 state so what I have you know two coins in a channel what this means as I believe in the future I will be able to withdraw two coins from the channel it's not really anything other than that okay that's so like an example of this or seychelles I see on check verify these an n-channel which is usually doesn't involve a multi-sig i see that i've only size science of a certain state usually the one with the highest nonce right and you're sort of traditional aetherium style and channel i make the assumption that if someone tries to drop an older state I'm gonna go in to bring that state forward and dispute it and they saw that loads through things I can make an assumption based on that of course something that I will be able to withdraw according to the state s okay does that make sense to everyone questions comments concerns okay I'm going to need questions at some point so you guys good luck love okay great so we have some fun you know some fun formalizations that we can make around this which are very reminiscent of like things of the CBC future so here's the interior watching right so here like the universe or the and based on that sit there's some subset on the next blocks that come up here right these are here and based on the details of the um you know maybe you can't unlearn money for example if you set up the zero address it can't come back but it can be sent to this your address if it hasn't already so here's somebody being burned and now you know that these states are no longer possible because this is the one that just got mine right and so he beyond you know consensus algorithm that we call a theory in themselves and either is progressing through this futurist cover of the material right which is say sort of borrowed from physics you know for all that the mean is not giving that goes into it and this is what we're doing right so this is one thing that happens what's the only thing that happens the other thing that happens is we have this local information write us about our passing things around signatures inclusion proofs we've got local information to yeah it's off chain right okay the last thing that we do is we make some assumptions right so the EDM set that says that some set of future states are possible right this is a pretty large set and what I do as someone who's trying to make a prediction about future el Tuesday is if I make an additional assumption that is not inherent to the EDM okay so here imagine sort of to force of the botching right so so imagine that we're at a state right here and someone it maliciously tries to withdraw some money okay I will assume if I have a channel talents and I'm trusting that I have a channel balance that it's so put in the future this thing will get disputed right so what that means is basically what entities I'm looking at any such chain that where no disputes have occurred and I say I don't believe that this is going happen it's an assumption it's an additional quality of the statement and it's an assumption that you make the valid mistake right so we can find those two things we did something like this right you have the finalized box that we saw before right behind me we have the same as here in futures comes before but now based on this layer right so these things which are possible a part of India are no longer possible according to my assumptions because I believe that I'm going to do something about them that's usually the assumption right and this is what we see and furthermore one of the things that gives us the great scalability I etherion is that these this pump does not just restrict as newbucks about it actually restricts as messages are passed around so if I get a new message and it tells me I can do a new to speak this narrows in the code of future states that I'm assuming are possible so we can call this our optimistic futures okay with me so far yes not excellent questions I got a question yes castle there you go why can we assume that that's going to be missed it's content but lightning is that someone doesn't have an outside motivation not to result correct say ah so that's a great question and so you know extra protocol incentives I talked a lot about even later on and certainly in layer 2 and they're not to bury a research and we need to continue researching these things in general however we we believe this because we think that black chicks are meant to be sensitive system so usually in layer 2 we use the properties that we're assuming that l1 fulfills to make our assumptions sound reasonable so you go through the work world right we have this decentralized Network where anyone can start you know bringing some electricity to my nook and because anyone of the world is going to do that I have my fingers crossed that in the next you know whatever the dispute period as the blocks are at least one of those people aren't had to be willing to accept my transaction now that's not we said that there aren't like important nuances to be analysed here so one one-line critical example of this that we have to be careful about is what if the dispute to keep my money safe cost me more money than the dispute itself cost me more money that this fees can get you right so that happens we're in trouble so we want to be careful and design the protocols carefully so that the the assumptions of makers reasonable as possible and ask another question you that was one nightmare over that looks like it is not fit to be more but in this Dominica oh what a swell a segue what a segue is this mystery - you're totally right so unfortunately we can't just write a computer program that does a four loop over all the future if you're in states that are possible it checks whether the analyzer assumptions this is computationally infeasible right so this is a great tool into when we describe so far it's a great framework a great model for describing how there are two protocols that existant work but you're right that it's not really useful in constructing some sort of layer two client that is like unified or magically combined everything in one way because this is a very very large set in fact infinite now maybe with the gas limited like the fact that there's only so many bytes it's like actually kind of finite but there's like way more atoms would you know way more than atoms in the universe worth of these things right yeah so exactly right so what we've been doing here is we've been looking at later to write this framework that we just talked about is a way that you look at layer two systems it is not however Granick that's useful in a building a layer two systems right but so this is what we really want to do right at the end of the day research should be going to fight motivated by actionable things and what we really want is to be able to build a layer two protocols in some framework that extends beyond you know a particular plasma researcher who has intuitions for plasma does and a particular channels regions researcher has emissions for channels two and so on and so forth we want to try to unify this under one sort of shared frame right so we want like when I like to think about dispute Legos right we want some way to contextualize and instead of replacing so like a plasma for example we're feeling very guilty of this we have like limo swaps and about and you know the job isn't all these things I think very very useful for us as possible researchers to be able to talk to each other but they're not good what if you want to bring someone you want bored because we have to teach them all of this stuff right and what the people who want to be fun to do understand is like logic and math and models rain so we want to be able to push that and so that's what we sort of the goal of what we're going to do here today great question great question so we want to be able to build things because the space is just too large it's basically infinite you know for all intents and purposes right this is too big to compute here we go I wish you'd asked at once laminator on/off switch we really wanted to put this slide earlier but you're exactly right right so we want something that is easier to cute but we also want something that is flexible enough to go the protocol right so for example there's a layer 2 protocol that says I can burn all of my money whenever I want and of course once it's burnt you're never going to go back from a B number this is a very useful protocol right so we want somewhere in the middle between the spectrum of just like before leaping over alternative boxes can be done without you know magically infinite computer and something that's actually useful so that's what I'm gonna try to pull out here today ok other questions other questions all right so let's talk about some hits ok I pulled these from a couple of different layer to sort of the science and protocols so in the other right here upper right here we have some localization this wrote a paper called note costly to commit chance very similar to plasma so they have a whole have this notion of local information right it's the same thing that we were talking about before a few slides back on what we call the high logo they're using that in their paper boom ok now there's another there's another hint that I'd like to share which is from the generalized state channels paper so great they work by the counterfactual team which is now been unified across almost all state channels porphyria this is very safe there's a for all here okay I like for alts and you'll see I mean talk about for all's a lot for the rest of these slides so there's another hint for all so here's one from my coworker my challenges this world has no paper and there is no sir no challenges right it seems like decisions are primarily based on challenges one person says one thing and other challenges it with another and it more advanced protocols we even have several layers of challenges where maybe one guy says one thing and another guy challenges and then the guy respond the first that responds again okay so here are some sort of these these are what I think are hints that will sort of lead us to being able to construct something very useful ok that makes sense questions there ok everyone has a TOC slide that talks all hi mind you one of the word that I love from history which on the island I guess I'll read it not to insult you all without a little Bachchan organizations have to move existence it's group of in existence the ability prove the message and see what and all answer depends beside other messages sunshine has not been published yet so this is very often a property that we see in our LG protocols someone makes a challenge and there is a possible response that could be made but after some time out that response isn't me and we take that as to say well this must be the response doesn't exist ok and so existence particularly is the word here I want to pull out so we've seen some challenges you've seen some for all's and we've seen existence and it turns out that there is something that has a lot of those same words ok so it's most first-order logic right this is your answer Lawrence or not this is her for all's and your exists so what we're going to go through them in the rest of this is we're to look at this within the context of layer two right so we looked at this for a while and it was very interesting to us as researchers that there were sort of analogies here and we came up and tried to come up with some designs for how this could be sort of integrated into altitude from fact in practice took us to ultra it took us a while to hit one that we thought was pretty solid but a big big key moment that helped us understand this was response I called dialogical logic okay this is related to the broader Kill Bill game semantics and I started this talk by saying game semantics right so dialogical logic is an interpretation of these first order logic sort of expressions and in evaluating whether the truths are possible by interpreting each expression as a game and then interprets truth of this expression as the existence of a winning or losing strategy for the equivalent game okay so this is very interesting and just for context of semantics it took me a long time to figure out semantics methods are not really you know I've never taken a semantic score sir so semantics is like meaning like so first-order logic like there's actually lots of logics which are sort of satisfied by the language that uses for all and this ranking so these are very important by the way so remember the outside that a is like for all of the I don't know line for those I already knew the backwards to use exist like this one just like inverted letters what's up otherwise they so so it's worth understanding that there are different semantics okay for the same sort of language of persona logic okay so next I simply example this is like classical logic is the one that you learn in logic 101 is what I wants mirror with and this is this you know where you can prove something like true or false right there's also called intuitionistic logic which in turn size does not it was like philosophers arguing about logic it's saying we don't like this thing called the law of excluded middle so in classical logic for any proposition P you can say P or not P right you can end them that that's decided to be true sounds reasonable rights leads to true or its false but apparently these phosphor guys will have aluminum can begin secured files like maybe something not right and so intuitionistic logic is like a version of logic which removes the ability to say room or the R P or not P ok so these are semantics depending on how you interpret what the language means these are called semantics and so we one of one of these for layer two so we're gonna call out optimistic game semantics because basically the way the layer to the scales is you might give you an optimistic property and assume that everyone's going to play long and so the blockchain has to process less information for the total computation that went into the state machine that was running off chain of day that was making these optimistic decisions okay so that was a lot so I hope that we have some questions at this point time ah so that's them the rest of the presentation give you a simple example okay so illogical was it on this later but in logic they're these things called atomic predicate okay so it's very simple atomic predicate slickness right right like you know one equals two is either true or false I think it's false yes and so on and so forth so here just gives another example of an atomic try to hit okay verify signature okay this is another example of an accredited okay so in state channels what is a state channel well you could build a state channel out a multi-state and thankfully the cleanest multi-sensor this is likely going to be two channels so here here's an example an intuition for how we're going to bistec there's a you can write a function to verify multi-sig right this is a time try to get that verifies a multi-sig so let's say there's like some participants right I'm gonna call these PT PS because I'm a to get writing okay so let's say there's like five participants right we can write a verify right multi-sig right which takes in the participants right SIG's right a message being signed right okay so this is another table of atomic predator right I think that value isn't your fault would it be nice if it's something to redefine this thing we could say for all P in participants verify sick right okay so maybe hopefully that's an instructive example so the idea that we're trying to do here is we're trying to pull out these sort of very very like very large your monstrosity Frankenstein layer to solutions where we have to write a bunch of custom things like this and try to like convince them down into a composition of these logical statements okay so we want say for all to the P in participants verifying the sync of that individual P and so this allows you do not like a verify sit and a verify multi-city you just write a verify see so they hopefully that's hopefully time great other questions the logic you talking about is strategy a winning strategy listen even for a game what does that mean okay so I'll get into that and so maybe I'll just try to provide an intuition now because I'll have an actual like game tree example soon but what that means is we take the logical expression and we convert it into a game tree okay I'm Tilly let me actually let me let me go let me go on the side so here I wish you to switch to this slide immediately because this is within the answer in the first question here are some intuitions for lettuces there does not exist such that this is an example interesting layer to eat and logical composition right for a lot such that the signature satisfies x and y right be honest this is this logical connective and yet you have to be really careful about there does not exist a signature in systems like this because there exists a signature right there is some string admits that's a valid signature absolutely so this is a great question and not to just illogical omniscience this is the problem that we face so in theory all Caesars is just in theory late from a lot of perspective all hash functions have an unlimited number of preimages that satisfy the given hash right so we're going to talk about how to solve that problem and one of the important future works that I hope will take I can get out of someone in this audience is to do a much better job analyzing that than I can because I did a big bad job and there's some minimal approach to be able to get this thing out there okay okay yes so we're very careful about how we construct these things but we're doing it in layer 2 is anyway so it's really just thing that's been careful about how we do it in layer 2 but again this is an important distinction so even though even within the sava logical interpretation right a semantics there is a semantics for like the love a bit like precise logical expression that says that this is always true because like all signatures exist out there there's always a string in place but we're going to provide a semantics an interpretation the logic in which this can sometimes be false namely if I haven't said that signature to anyone else so right I mean one of the standard approaches is to talk about a party having knowledge of a signature correct right which is a different kind of statement correct so so so there are lots of approaches to knowledge so I I went down a long rabbit hole on this and cycled Kripke semantics which which defines us in the worlds W you'll see something borrowed from that here in these slides defines an accessibility relational way to progress through world a world is successful if it's in the we want to talk about temporal logic to do with time and and there's one for knowledge as well and so on and so forth um we're not going to give a rigorous treatment of that here well we're going to talk about today is just the first step in sort of in sort of formalized novell - which is let's just look at the games let's just look at the games and so we'll do a very simple crappy job of the knowledge that is not rigorous and I don't think you could prove hopefully there's someone here or at DEFCON that I will be able to talk to that knows more about University's ability and these computability assumptions that's gonna be able to inform me much better than I have I have so long I'm lucky enough to see a few of those spaces in the crowd and there's definitely more to speak - so one of the one of the goals of this work is to be able to pass that part off to someone else who can do this much better than I can't because I you know I you know there's only so much time in a day and I can't but I can I can train home okay so other questions excuse me I should not have done that yet other questions again the goal is to not go through these slides guys I'm telling you guys what is the successful stay here so ask for it ask away okay but no questions so let's get into it okay so let's define this language Duncan worked with okay it's very simple for sort of language okay these sides are called quantifiers okay this guy's for all the upside down hanging inverted angry - its mirror you know this is your 4 L also known as universal and complication this is for ahlet's and sort of the universal this is exist it's called the dual of Porto is existential quantification so for all right so we actually when we write this in practice when you write something like for all X in an X ok I only write exist X in X right and then we say this is like it such that another like some T of X right some P of X now they have notably in most logics the these two parts the duals of each other so not so this is this stuff is good we are not by the way so not for all not is the same thing as exists and not exist that is the same thing as well ok so that's just who she anyway so then we're also going to use and ok so you're sort of upside down V or you know I'm free to be whatever is we've got the same problems in Reverse upon a fire this is your aunt this is or not this is your war ok good make sense yes yes ok excellent ok so I'm going to briefly talk about simplifications that we will use within this language so there are these I repeat over there that was a quiz natural so P and P sub 0 and P sub 1 are going to be our our summons for a generic proposition okay so this is any expression in this language which evaluates to true or false ok I think that means it's closed so there's no variable floating around in there all the grandmas or mobile pod and it's well-formed ok you know you know the street not not was nothing after it is not well composition it's just like this we're vacuous statement that has no memory tonight yeah okay now along with with compositions we also have formulas okay which accept as an input some variable so for example x equals 5 is an example of a P of X right P of X you know that's re X greater than 5 and this example of a formula because you can plug in different actions that will be true or false and they're free in X right in cents a room excellent okay and I'm going to use a script notation for P of T so this is a little tricky but what we're doing here is we're plugging in 2 for X okay so right there any more consumers and I can scream onstage but for example for the P of X X greater than 5 P of X / 10 would be 10 greater than 5 right which would happen to be true right good make sense make sense questions comments concerns school education is just the particular evaluation of PD where X is equal to correct it's a particularly you plug in in your summary actually it's very hard to see fun yes okay okay well apologies for that please shout out if you can't see things and we will whiteboard them where I will go out of full screen and zoom in or whatever to make yes exactly so in fact why don't I just no need to do that so P of X can you can you read that maybe that's the same exact size oh okay so we've got some peanuts if so to DMX let's say P of X we've defined it with a dot dot equals this thing is x5 then you know P of X which directions they can slash given X / 10 would you know would be would be equivalent to 10 greater than 5 okay so we have X is free here and now 10 has been subsidence of impress okay excellent excellent [Music] the very right absolutely yeah I'm sorry it's this tough life or is this okay yes well let's read let's read it out loud so there's actually two there's actually something just outlined in Section two so are even today as a batsman who the straining yes so this expression read analysis for all X and X so X look little X in big ax right so this is the set the domain of quantification few days okay and this says there exists X in X such that P of X okay right and so what we will see right well one up seeing is we're going to be we're gonna start building up disputes or sentences for all X in P of X so we also can say I have this X and I'm playing not to P slash but you know whatever the special cases they're that they're kind of discouraged I just okay okay other questions excellent and how are we doing on time oh great I don't think we'll finish it's been touched where do we get out here 3:15 no okay let's call it 350 okay and then the last thing that we're going to cover in this language which remember we touched on the floor you've got a target proposition so if the other things too small this is definitely small but it was like what's a simple atomic proposition in equals so actually that's a bit of a lie equals is that it's like really connected so really five equals ten that's an atomic proposition and evaluates to false right but but things worthy where both sides of the equals are filled they come an atomic proposition greater than there's no example right less then there's another table okay I know there's there's three in particular which are very interesting to us building layer two things which is is this thing the hash tag image so it's this little H the hash English to this big age which basically is equivalent to saying hash of blue H equals H right these are the these are these are these two atomic propositions well we have lights turn off right okay and otherwise verify signature right so we're all familiar with signatures in the Wild West of cryptocurrency which is a very fun actually you can build a signature of the hash function it turns out Lamport Leslie I'm quickly at night and the last thing verify inclusion what they were to verify inclusion of the thing ever this of all the functions that are evaluated to true or false the coming position any function you can imagine so I have only has it my intuitive answer is yes and I think intuitively you should think of this is no no actually okay so no literally the important thing is that it is free of these logical connectives ok so if you have some fans and some nonsense ores or some quantifiers this isn't so a and B where they are two atomic propositions is not a prominent that might be breaking it's possible I'm not a super super deep logicians it's possible or that that's broken but that's how I think about it well the big one that's that that is makes it an odd proposition is the not happy for all it exists right not having classification that's that's that ends up being the big one yeah great question great question so anything that arrives at your Falls as a composition an atomic proposition is one that doesn't have many of these these bad boys Americans these are sort of indicators that there's more logical structure beyond just some sort of simple function evaluation the reason for the consistent use of language we're like I mean the atomic propositions like is equals who is has payment for all semenya instead of like that is valid signature you have my very time signature which stuff but it's certainly my accent inside the Great Hall so I dunno I should I should paper to have more consistency there yeah and I was actually the most egregious I had to say the initially reported breaches in consistency than that which is that I shouldn't have in the parentheses here and you know signature message punky and I should have you know before inputs to verify between but absolutely yeah so that is that my bad my bad but hopefully hopefully can see it the point across yes are there quantifiers you don't like because like if you're considering like atomic binary values those are like bullets like built it is express like player I know with that there exist age so that and you're like saying like knowledge you want to know the moment knowledge people on fire yeah is that what you're saying yeah so I this is why I decided jam with you after this bi because that's totally a dollar question so there's like you can think of two layers happening here okay so the layer that we're going to covered mostly in all these slides is the on shame layer okay and there's there's a relationship to option that's not as well defined off chain is for on chain well we're doing is we're just building the dispute games that go on changes okay so what we're gonna end up doing is going to try to construct a contract that sort of implements the ability to check the truth or you know false evaluation of these things so is there a more even less classical logics than these ones my knowledge or is your knowledge is actually ends up being stuck want to fire that that's absolutely right we're gonna ignore that for now well we'll treat that very simply block will have something called computability model it's not as well formed as has to be like you know very very well quantified but you're absolutely right but for now for the intense purposes of this all we're going to think about is for all and exists and it should be noted that there are many extensions with semantics I'm going to come here and so for instance the binary search game which is the true that guys use I've messed around with right here that's and for all exist for all exist but I'm not sure if it doesn't denote its own on a fire or or we're connected maybe do you want that okay other questions before proceed all right let's get to it so what we want to do is we want to take these expressions right things of you know the performance under there and we want to turn them into games okay this is our goal we wanted to so these lateral expressions we want to evaluate their sort of truthiness whether they're true or false in relation to some game okay and eventually the goal is for this to be a game played on chain it's going to correspond to the dispute contract or the deposit contract depending on what layer 2 protocol developing mask so we're good for now we're gonna talk about two players we approve of key an opponent oh okay that's not good and summons a and B capital A and capital B are going to be variable as representing either the prover or their punt so today is not equal to B but they might be one of the other okay does that make sense so very often we want to talk about a player generically and we want to talk about the the other player generically some will call on a microphone everyone do with that great okay okay so these are the two people that are playing this imaginary game and this game again is our interpretation of the logic it's what gives the semantics the meaning to the logic that we're gonna try to make him to player two constructions through good great okay so there's a game station so a game stays a tuple of two things a player remember a but he says either this is either to prove the opponent but we don't we don't care about this you at this point we know this the defending player okay now the only thing here is the current proposition you can also think of it as the prophecies should be defended by the defending player okay so this is a state of the game okay so the game is currently in some position there's there's going to be a defending player specify and in current position specify right time to just I'm good they're wrong and what did I say here okay absolutely say that somewhere is okay to the people that that can't be oh yeah so if you would speak we might say that this games a just a sign that I love this this is something that I found in a lot of game semantics and logic so an eighty science state is one in which a is the defending player just just an additional that I may or may not slip up and use through the wrestlers presentation okay that makes sense everyone right pretty playful okay so the next thing we gotta find now that we know with the state of a game can be we want to talk about how the state of a game can progress right how does it move through the iterations okay the way that we're gonna do it turn-based sequence of challenges okay so this is gonna be one game state okay and then something's gonna happen this is to be the new game stand okay and Sonny's gonna happen this is gonna be the next game state okay okay that's unreasonable everyone makes us right and know that these are different propositions okay so the I believe this is p0 p1 and p2 right these are gonna be different expressions make sense all right I always like we're between B what's that always back and forth units always but always turn this yeah always turn this and one thing that's important to illustrate here is that the semantics and I'm going to find I know Sebastian depending on me immediately after this for saying a bunch of things that don't reflect some of the nuances of things like haqeeqat strategies love you strange things in very developing semantics but this is these officials provided a this will be sufficient to provide me some intuition for why this is possible and what the contract that we want to know what you look like alright so for our purposes for the through the purposes a says something these days now something else is not something else something else and so on yeah does that make sense okay now we get the real meat and bones okay this is like the bee's knees up over to talk about here let's define the rules from which a p0 goes to V V P 1 ok so here are the rules rule number one okay well first of all just talk about how this table is ok so this is a game state and now the opponents will be here might might or might not have to make a choice might have to make some provide some input okay in this case they don't and this is gonna be our new resulting state ok so this is our this is our thing if you love to pair up everything to the right of zero and so we call these challenge rules this is how the games no progress in the steps make sense okay so it's first shondrel it's very very simple this a is defending a statement of the form of not P then B may challenge by claiming P okay makes a lot of sense I say that you know the the sky is not blue and my opponent responds with well in this kind of blue okay makes sense make more sense than they say it's B&V said it's not because I say I have a balance of 50 in peace if no he doesn't great question so the reason that we want to avoid that is because what we want to do is we want to slowly take these very complex expressions and reduce them down so for example if a kid say P and then you could say not P then n could say Takaaki and then you could say not not not T and then see if you take not not P right and so all we're doing is growing this leg logical expression what we really wanted to make the expression smaller because we want to get down to something eventually that we can evaluate on chain very easily so that's a great question and intuitively this makes sense because I plan a you can play my game but what we want to do is provide in such a way that these games sort of reduce so the two lands of the movies that great question great question but here's the intuition is there yeah I guess that the game can transform in a way then if one person says something the other person says something else that disagrees so that's exactly great intuition okay does this rule makes sense nice here's a final a a says p0 and p1 that I has a that that B has a choice D may either XI 0 or 1 which is the left of the a hat or the right of the end and B says not P i okay so here's an example of where not does get that bond regularly produce me and into something else right ok so hopefully that makes sense it's very logical today says the sky is blue and it is raining then D they either say the sky is not blue or it is not raining right this is how this is how they respond and so notably everywhere to be here then the next then this rule would apply right an a and B are sort of switched out right but now but now we would get these a over here API over invited so this should give an intuition for how these games are the best right okay here's another one or right so lord is something that are you doing through the rapt estroux are the right is true that it's true so what happens in a cesspit 0 or P 1 then B has to respond by saying not p 0 and not p 1 right so the only way for this statement to sort of be false is if both of these things are false because this is what the order does is conjunction and destruction there's thing like that any budget right so does that make sense it it's bigger ah this one is bigger so it is bigger that's true but now it feeds into this rule so right so so normally like you know this this outcome has this rule about it and this song is in that this rule applied to it which will then get that this rule applied to it so what we'll find is that you've got this one kind of looks a little bigger because there's now two knots and a half as was just one more eventually things will would you stop will always get smaller and smaller incisions around later vision say that's a no he's not that you didn't report our position yeah it's a some intuitive reduction the goal is to eventually around so we're just like checking one signature right so the verified multi-sig example that i gave we want to say for all P plus the participants right the great thing about doing them all to see this way is you can disprove the multiset not by checking all the participants but by simply providing the one that's not true okay and so this ends up being what happens a lot in with being in layer two protocols for example a plasma you make a rule that says before all blocks less than the line exiting from this condition is satisfied would be very expensive and it would break the scalability or system to check all those blocks on chain but instead you only check them into the true ones that people decide to respond to okay so here's here's a fun one okay this is this one things maybe get a little more hairier these are these are pretty straightforward now we're gonna throw in the two qualifiers the first one we'll talk about is the existential quantifier okay so there's a such fun part let's just let's just read this statement a is defending the proposition there exists X such that P of X okay so how do we respond to this the way that B is a lot of respond to this is the same uh-huh I disagreed for love of X not to do this okay so this should make sense so if I sing every day in the last year there was a thing last year when it rained okay so what else to response in you know every day last year it did not man okay so hopefully hopefully that makes sense it should be fairly intuitive and again these are all very intuitive right we're just providing a particular formulation so that seems very obvious right there's nothing very very hard what the counterintuitive about these rules okay so now we have the last one and as well as the caption that you thought that prior to the universal inspire and this is this is oh this is a big one so if a says 4 X P of X B may choose a particular T and s and say not P of T replaced in X or or if you replace the protest ok so if a player a says it rained every day last year player B can say it did not rain on January 3rd of last year right so the this seems very important one is one of the things one of the main things that gets us the scalability of these solutions is that oh the old we can evaluate whether something is true for all of these things with this dispute assumption by simply only analyzing particular ones that people are claiming it's not true for so this is missing this is the really between the meat and potatoes of our scalability under this construction yes could only be used to rules lead to infinity challenges ah great question all these will see different challenges my gut says no I don't approve for you so I won't say that absolutely but my gut says no and I think that was I think that would hold up and there's lots of results so this is by the way I'm very very close to stole this from this dialogical logic things very very very simplified logical logic and the biological logic there are lots of results that say that a shrimp I sub antics that are very similar to the structure and a few differences very similar exactly correspond to things like classical logic there's another version that corresponds to intuitionistic logic there's no that corresponds to linear logic and all these other in bubble I think there's one for you dependent types because gravity types are also logic time but I believe that there would be a result I would say this rule introduced and there would be a mention and when you think about it they kind of make sense these things are sort of getting smaller and I don't see any place where we would start looping through anything sorry could you speak up over it sorry new conditions need to thank wait they so exists turns into a for all when a floor off is not turning to exist of world just gets rid of the four ball and puts it not in front right so so so so so maybe make I'll just do a profession out okay so let's say someone says exists X impacts and such that few that's okay and let's say let's say it says this and the next thing we would have you would have be same for all X and X you're next and I knew that a said again they would pay particular team and I would say not not of tuna okay the particular images yeah so they so the for all doesn't look back you to exist so we're okay we're good we're good no internal loops as far as I can see which the PT is not DT than us so the middle one says let me just read this off he says a says there was a day last year such that it rained B says for all days last year it - not great day says it did not not rain on January 12th of last year okay the person that not not will eventually resolve in the B st. not Pete and then a sink as we respect it not not reduces to Oh screen height other questions like this the challenge game below YouTube and attracts like brings I believe someone says that or all previous blogs the statement April and then the other guy said oh it doesn't hold or below zero and they never guy said no it closed for well zero but the other guy said oh I actually meant doesn't work for block one that's great questions so just to rehash that one can hear the question is do we allow a sort of replays do we allow to be allow if suddenly maybe some guys those for all blocks some guy says not for this block but really it was not through this block and if we went back through this block we might get stuck down this wrong trail when the right trail is over here so we have a contract design that basically makes it so that a and B B's prove apart really piano the Rural Employment are like these sort of imaginary players we replace that which was one in which anybody can sort of play on behalf of piano so we go is from lunch string of plays to trees of plays and so this allows you all 20 people to these people all the blocks all in parallel and it works out to a great question great question others cool okay so with that there's one last thing to cover which is what the heck happens at the end of this game right that's the one thing that we haven't gone over what the hell's going on as the end game outcomes so the game's gonna add when we have an atomic proposition so for example over here if we assume if the P infinitive hog proposition the next thing we get here was be saying not P of this thing right and then we have a saying P all right and now we don't know how to reduce it any further okay so when we can't reduce them any further this is what the game is either won or lost okay and it via the outcomes that you assign is quite as you'd expect if a is true so let's say the game states of the economy we didn't say this ba right so again because one player either to prove the opponent we don't know much but not the same as aim and sum of atomic proposition names so I have a little aid for this atom okay so the game then if a is true right because again atomic propositions have a truth value associated with them if a is true then P wins right therefore in business but really be 10 men right because if you were to actually play the game we could make a mistake and lose ah absolutely right so we'll talk about that a little bit more later but for right now all we're going to be doing is talking about if the game had ended this way so what you're talking about is the behavior of how people play the game so if I say for all things last year I could definitely lose the pea which day I'll take if I pick the wrong day right and this matters because you can't if you actually play the game between two players in a real system you can't go back and say well a 1 therefore a must have been right in the beginning that's correct so you so there actually are layer 2 designs that correspond to doing precisely that and I actually think that it's a pretty reasonable design so it's too much of a sight trying to get into that all now but there are cases in which maybe you might want to be lenient in that way it does give me some advantages but it is a good point I mean from a security standpoint you think the fact that a that the fact that they won the game doesn't establish that little a was true in the beginning right so you would need an additional argument about incentives somehow absolutely so you would have to get to any kind of conclusion absolutely right however if you make the assumption that everybody knows that if any game plays out that involves them in some way and it's one than we assume all the possible sub games they could have been played out would have been one then that's okay so there's nuance there and I know and I know that essentially maps that you can't go through multiple turns it's only like really if a game was won all possible challenges would have been lost that's really the assumption that you can make that other letters your protocols make but it's not correct right if you and I play chess and you win right it doesn't mean that well it could it doesn't me that I never had a sure win position on the board it might be that I actually had a winning position I just missed it right so this is the case however there are some where this is a bit of a science so I'll try to keep it relatively sure but there are some cases in which you can make that and particularly we're okay making the deception if we tell you ahead of time hey buddy your life depends on this chess game because every other chess game is you're playing next in the future is gonna be dependent on whether you it's okay if I suffer because the game came out that way but if everybody else suffers because I messed up the game very truth that's a design problem very true so so so some of the major design problems there we can tackle and the ones that are sort of a you know contextual subjective decisions you might want to or not may want to make or not make it your layer 2 protocol those are choices that you can make yes oh is it a game that you're playing a game on the results of a game those already played in which case like we already know who won the chess games so now you're planning gameplay did you win the chess game around it but even so if then won the chess game I night he might mess up then we play a game about who really won the chess games if he makes a mistake I could win the second game and convince the room even though he deserves it so like one claim one pain pain doesn't mean the it like the country it's not Monticello right that's maybe an illuminating example I think I think we're kind of short because there's there's a whole separate discussion what we're doing right now is pretty separate from the way that you implement a contract and so one of the key things that you want to do when you turn these semantics into labor contract that you're writing out blockchain is that if someone else makes the wrong move and you know that they're making the wrong move you can't let that screw them over you have to be able to sort of go like start and use up a new game from a different point in the tree where you make the move that you would be this right and so there's a contract design that allows you to do that but anyway maybe I'll take you here because this could be a very long discussion is what I want to have but I also I said I didn't want to get thrown aside a couple more okay so does this make sense to everyone you're defending some games and you're defending some think if you're defending something that's true you won if you're defending something that's false you've lost that make sense cool excellent okay here we go okay so now we have a game tree now we can make the game tree so let's let's let's define two atomic propositions path entity what will they will then how will they be assigned your thighs you guessed it that's as falsity is true okay get it on read this by the way it's possible some pink enemies okay it seems like we're gonna get great so daintree for false more true so the game always starts with the proofer I haven't mentioned that yet but it's pretty obvious the game is initiated by the prover that's the one trying to prove it so they made the first defense of the thing being prudent okay so false or true so P since false or true now there's only one response according the challengers though which this is a not false and not true right so that is according to rule rule number three here right right here p0 uh not be 0 Anunnaki 1 right so false portrait not false and not true right make sense ok so now we have an right and so they add P Naza choice P can either say not on the left or not to the right ok so let's say peaches is I equals 0 aka the left now P is going to say not the thing on the left which is not not false okay and of course not not falsely mikey is by not false by own which is by false Mikey right and so of course this day Malcolm is going to be 1 by oh right so the reason that it's one is because Athens in the time proposition it's false because P is defending a faucet on proposition it's 1 by P so does that does that side make sense yeah great okay and of course the other side the kids were one which is this tightly to those big and someone says not call Sam not true well you should obviously make you know go ahead and say not true right because that's true so yeah not not true the same thing happens when you're the sweetest is not true where's the truth and that's what Mikey okay so for false or true we have now taken this expression this this expression in the syntax just the language of first-order logic and we've interpreted it as this tree doesn't it says everyone is the one here awesome okay so that's great so now we've defined a tree but we still haven't answered the question what does it mean for this thing to be true or false we've interpreted this expression as a tree now how do we look at this tree and understand whether or not the thing is actually true or false right so that that's the next question organized and the answer is going to be strategies okay so what is the traffic and I promise we're almost through the good stuff finally into protocols some plug all right so so of course a strategy is a subtree and actually may be able to skip to the TLDR of the damn shot to you which is a strategy for player a is we start off with the big thing and they look at all the possible challenges that you can make right what's everything that B could say if I said device if player a said the first thing right so for all the challenges we know winning strategy says it says all the challenges that he could have done a have a response to that I have to be able to deal with that case so you look at all the challenges by B you speak my specific powder challenge but that should say so you specific pick a specific kind of challenge and I'm offline okay I think highlighter in there it's a I promise you I said hopefully I didn't present again oh baby okay all right no worries my bless my phone died we're gonna be good okay yes so my strategy is when player a says okay I'm playing a having a witness what's my strategy here right okay my strategy is I'm gonna look at all the possible things that P could do I don't know people what I'm gonna do in response right and then for everything that's done in response what are all the things that they could do in response to that and for each one of those I'm gonna pick some as well okay and so this defines a strategy for player a right so for example let's here yes what's leg was that Polly six thanks a lot I can fix it okay right and that's when we repeat this process right so let me let me just start the board because maybe board as many this one here it's on a high level what is the strategy let's let's Li get a strategy for the prover P okay so we have some some root stage here I think this is you know P you know whatever I'm not gonna write out this thing probably examples right but what is the strategy for the privity a strategy is we look at all the possible next nodes in the tree right so these are all of the things that could be played by oh okay so these are all given form Oh something oh something else something else right and so P has to be every every single one of those right so every everything that oh says he's got an answer okay so what that means is we're gonna pick one answer for each of these that he's gonna play in response right so these were played by oh now these are played by people okay so he said one thing he has to be able to say okay here's all the things that oh they say and here's what I mean to say in response this is my strategy does that make sense it's what I am choosing to play in response to anything possibly I can play by my opponent and so again this different people for example imagine maybe you know maybe maybe terminates terminates here and this is like yeah but for this one there's more stuff that could happen right so these are all you know you know counter counter counter claims by oh now again he has to be able to nominate that you need response these rules okay so in effect will be debt is that you know perhaps Oh couldn't make this decision work you know this decision as well can make these books but we want to pick just one right so this this has to be chosen this has to be chose missus we chose this has to be chosen this has been chosen this has to be chosen assumptions listen to these are on week and then all possible plays by an opponent have to be have to be a numerator does that make sense this is a strategy anything like what it does this is one gonna do anything he does after that this is what I'm gonna do right down to strategy because this makes sense questions comments concerns all right well let's have it a strategy so we just did the game true or false or true okay and it turns out that stretch is very easy to look at it turns out that our strategy haha what a shocker is one of these so normally this sub-tree or this subtree on both strategies okay the strategy here kids I've been pretty easy because we've got a lot of knots here we've got a lot of things where there are main choices to be made so in pieces this only has one response so PE Husson but but but now for for for most response a strategy for P has to be to choose one or the other actions America okay so let's say P's gonna choose this action okay now of course we have the response by oh and then she chooses a response together now there's not many branches here right so it's very easy to see that he was doing in this but this is a strategy there's a basis everyone helped us with this strategy is this interactive or not interactive so the this so this this without any highlights this tree here is the full possible set of all interactions okay so these games are definitely interactive like they're meant to be describing piano interacting or challenging and Patrick childhood kamikaze right so this defines all the possible actions okay a strategy for one player defines the specific action that they are going to take that they could take in response to all possible actions by the other one okay so every time we show a strategy routine every time we have a play by oh we didn't write one particular response might be so it's my strategy like shows which one I'm going to do okay so realistically like oh would not send that first one he would just jump down to the last time he sends an interaction and then people private correct so realistically if you want to make this an efficient smart contractor you don't have a timeout through this part this is more of this look so in reality obviously not not always reduces to not and not you know not not yeah not as reduces to the thing and not not always reason to the thing but and so obviously personality test into one dispute period in the actual smart contract innovation well I will ignore that for here because we're just trying to get something from semantics that's like that you know an equation you know to take this like it in another example is similar to how like tic-tac-toe is a salt game and there is a strategy to always win tic-tac-toe exactly right exactly right yeah it's not like the the first assertion ie I don't remember what you call them but the first on the left side is like setting up the keyboard particular exactly right exactly the next steps are all the games but in our case the king board is not a tic-tac-toe board okay the board is AC is a logical statement and the logical statement progresses through each thing yes and this is why for a layer 2 protocol you would not play chess you would play tic-tac-toe because we always want to know that we have our money you don't want to have to compute enactment when you know I'm not infinite but a mass is exactly right exactly right now so just wouldn't be very useful in this room all eyes just all been about maybe a I saw up like all the games there's some gamers that's awful we wouldn't want to apply this ran into it what's wrong yeah so what you really have to enumerate all strategies I just enumerated and stop as soon as he finds a winning strategy definitely we do to have a securely I chose another for all that Varitek me you don't have to finally it just absolutely right like one strategy that leads to be out community tend to have and then absolutely right to do to continue so to have safety in a sense of layer to what we want to say to say that a protocol is safe in layer two is that the winning strategy can always be found by the person you know defending their money that's what's taking this deposit contract yes it's possible to be great also the different possibilities because if you have a graph that is huge like wind up with like just beautiful seeing also strategies and way to have a way to set one over another because always we take actress like maybe one little country just take the best strategy ever on this try China whatever so how do you do that on the really complex set of data so what we're not doing here is proposing that all logical expressions can be as a different layer to gaming that is meaningful most of the expressions that we interpret with the semantics are not gonna be meaningful they're gonna be on safe protocols and I can be useful maybe they're not gonna be able to move money around or whatever the point is that we can find some of them that do correspond to the player to protocol so particularly state channels plasmas things like Troopa and optimistic roll-up all of these things are very simple games which do have continuing strategies so like Carlos said you don't you don't make chess out of this you make tic-tac-toe something that is playable right so this is what this is what layer 2 protocols were developers were doing when they invented state channels they they didn't realize it but they were finding these sequences of expressions these challenges and responses in which the client could like have a chance at actually computing what's going on yes could you do something like turning a complete and then do a problem that department absolutely absolutely good so state channels are gay example of this I can play as a chess game in a state channel but the dispute game is not going to be about it is not going to be me fighting my winning stretch the chess game it's gonna be me fighting the winning strategy for proving the highest signed which we sign nods to the smart contract and that's the channel stuff and the chest that is a layer on top of that exactly right exactly right yes it seems like I'm being like finding the correct finding if you have a winning strategy for the for all it's got hard because you have a like you need to find a team absolutely right and so and so the for all in practice there's two ways there's two common ways to be able to compute for all so one for all that we can do keep for easily is if we say for all things such that signed by me or such that signed by me I know exactly and I can enumerate that so that's a nice for all another for all that we use in plasma is for all blocks less than X and now that we can numerate because we doesn't go with the X X minus 1 X minus 2 to 0 so it's a finite set and so absolutely there are tons of games here that we come up with that are not computable and are like very very hard to reason about but some of them turn out to be lazy protocols and so we think that's pretty cool yeah other questions great questions yes the way each step like he's stepping the trade felt it would have an extra pair and in theory each stuff without that is great in reality what you actually have mr. Turing this is what this is was mentioned earlier is only when there's a choice to be made so particularly the time that really ends up gift-getting you would hop to a dimension time up is when you got a needle for all or hand and you have to make a choice see they're not the left side and or not the right side at the end but but but you can doesn't you any pianist should design the contracts on that expression not got to you is automatically reduced to T because this is the only possible place so why play time on it can automatically be reduced yeah well in person like lost my I mean do more if you sell but if like every game has to share this day interior so like from the start to the end that have to be in this game can I have different gifts apparently yes so actually and so we touched on this in the paper MVP is one of the very interesting examples of games that doesn't rate into this magnetism planet not even new connected to do it the latke connected so to not be playing inside baseball here plasma MVP these are the original spec for plasma have this thing called an exit cue and basically there could be like transactions forged and inserted by this malicious music and the way that you prove that they were forged or delicious was you proved that the sum of all the UT EXO's that led up to the forest once was equal to the total amount deposited into the contract and so this actually seems to be like a summation operation so we would need to define some sort of MVP q observation operation so that has to be done been done this because there's a lot to do without that but you're absolutely right that's it that's a great example of more sort of game than their activity yeah absolutely no other questions all right well I like him so keep them coming okay we remember we okay okay great so this is an example of a winning strategy why is it winning because every possible leaf every game outcome was one Mikey so a winning strategy is it is one in which all these branches was on the way okay so if we go back here right buddy we liberated the so for instance tic-tac-toe has a lean strategy right because we can numerate all the responses by the button and then 1 pikmin particular play after that and so on and so forth a narrow one so if these are all one and this is a winning strategy for people because they've all been won right and so what this corresponds to in later two world is the reason that I know I have some money is because I know whatever however some tries to dispute me whatever they do I'm going to be able to win that outcome okay and like this is why I have some layer two states because I know winning strategy that proves that that state was internet so we can sort of interpret the truth of these expressions based on whether or not there's a winning strategy in the tree for that for the particular image that corresponds the particular expression make sense nice other questions comments attorney and so some interesting notes on this one of the ways that you can understand odd than not is it reverses the roles right so we have that not expression P right not paid because that not reverses the week right reverses the roles Marisa's so if someone trying to prove P then it's like the opponent is trying to prove a not be okay so this reverses the roles so there's a winning strategy for key then there's not one a strategy for o and if there's a winning strategy for oh there's not a winning strategy for P so thankfully we've retired that at least so what this means is that if P is sort of true because of his winning strategy then oh not people will be false because now the other guy is the opponent so there you have the winning strategy is now the one who's gonna win but he's now the opponent as opposed to the proven so this is this is sort of good we've recurred some intuitive properties of other logics and other semantics in which is singin a is true staining the statement not a is false right so we released with at least recover time okay I wanna pause for questions I don't have this I'll do it once again okay great but learn about photography okay so this is saying that we've totally ignored up to now and this is saying it does add more complexity most of what we've gone over here very very similar to existing works in game semantics and biological logic and these things the complex nature that comes about is in layer two protocols these the truth of a particular composition changes off chain so for example there's a game corresponding to a channel and state channel thinks it's right but basically the claim that says uses this multiple evolved multi signaling system before that says I claim that this is the valid state because I claim for of all states higher than this for all the knots is higher there does not exist a multi-sig signed by everyone and so that is what state channel is so let's say that that's the end that's true at time and X maybe at time X plus 1 we sign the next knots well now this thing that is false because this one is true here right and so there's some notion in in the layer tool that is subjective truth it's not that it's not like true or false which is obviously true right click this is the expression true or false duh that's true like oh no duh true or false right but the expression signature exists or hash tree which exists that's dependent on what the players know and what they're allowed to play exactly this this is the point that it's not the facts it's not that what exists abstractly changes the players knowledge - right exactly right so players knowledge about particular data changes over time and this changes the computability of what's going on right so we have a yellow we have a bottle for this right that this problem is called logical or missions right and so we have a problem for this and this is that we have a solution for this whether there's a problem beyond solution there we go ok so I don't think we'll play to you that it is nearly as advanced as the rest of the massive amounts of work that have gone into the systemization of knowledge and cryptographic knowledge and computability it's not but it's enough to be improved constant to demonstrate that we can express layer 2 systems has you know has logical expressions and so unify them all under one framer ok so the way we think about it is we define subset W and this is like a set of the worlds okay so one world it was that might say Alice has a private key King but she's not signed anything ok another world like saying Alice's s is the Viking king and she's signed message m and sent it off to the opponent so the opponent knows how's the signature but only on the message n right and so as we progressed through these world that progression so Alice when it started out not haven't seen anything and then at world zero and then a world one she decided message M this is what will allow us to change this thing between true and false because in this world it's not true for anything that there exists a signature of my house in this world it's true for a message that there is a signature of my house and so this progression through worlds is what you actually do when you execute a layer 2 protocol and you and you send them ie roundoff chain into it'll make sense so we can find this a little more precisely by saying there's a computability of computable subset ok so we call these X hop ok and this is like the segmentation but when you really care about as a function it takes in the current world and the which player it is either either the approver of the opponent and return some subset of the total state which they contribute which they are therefore the loud to play ok so for example you know in a world where Thomas has not seen anything but cannot play your signature as a challenge so if the world W here says Alice has not signed anything then executable is a subset of X which does not include Alice's signature and therefore you know exists such that signed by house will end up being false and of being false okay so tactus how do we how did this has to affect the game somehow so the way that we can affect the semantics is we change the final challenge rule right so we have this five challengers rules before the university lot fire for all it's not changed it so instead of T and X we can only pick tag team in the computable subset of X in the current world by the current player is going to be providing the challenge so this is a got a subset of the trees so whereas before all the possible things were known by the logic and therefore all the possible things could be played in history radical notion now we might say we're in a particular w0 due to this set of worlds and in this world you know you know maybe this was false right but in this world it turns out that oh can i play cannot play this branch so we're good right so we still have a winning strategy because in this world this cannot be commutative it's impossible to go to play it because it's computers only finite and though that only knows the things that it's downloaded off and because Palace is not signed any that has not signed the thing and there were economic endowment from the internet or cubed then this this thing is inaccessible so we restrict these observes theoretical game treaties which would - only once which are computable moves right only the only way to play something is if your computer can get in there and punch the numbers and plate and now note of course that in each will W there's a different game tree right so maybe hit W 0 at maybe of W 0 this was our final but maybe of W 1 now this is playable again right make you know a reason X there we go ok so maybe and maybe in this world it is playable again right so it is playable again well now this thing becomes false because the strategy doesn't check out right the strategy doesn't work because this is laws ok and so what this means is that as we progress through worlds these propositions can go from being true to the impulsive it's no longer meaningful to interpret the truth of a statement in a vacuum you have to interpret it in the particular computability world or whatever you want to call it that corresponds to the state of affairs right and so we say that now there's a strategy that is winning or losing even world done and therefore we say that a logical proposition is true or false in the world w it's not in a vacuum it's not the true or false on its own it's true or false in the world w XS so in practice the world W that you're going to track you is for instance what am i signing yes so in this example what the party can't compute is whether they would win or lose if they went down that right path or is it that they can't compute they can't even compute what the choices they know so what it is is they can't compute the move therefore they can't play it so the game trees so they don't even know what there's some uses they know what their set of moves is is one of the computer can come up with right so it's so it's so but they'd the but all right so so for example more importantly I know that my opponent can never come up with my signature unless I've given to them and that's the really important one and so that allows me to restrict the subject so you essentially you're taking the original train you're just pruning out that's exactly right you're pruning out any moves which are computationally infeasible to have been played in the first place and this was what removes the logical omniscience problem and makes the extrude hang subjectively so I have a set of moods that I can if in the game might one of the moves I could place to exhibit Alice's signature on some string right there's a set of strings of a certain length that I know I can play it's not that I it's not that I don't know that that I am allowed to play that string of bits it's just that I don't know that's the string I should play in order to win that I don't know that I can't figure out the enormous number of moves that available to me which of them is winning okay so maybe I'm more loosely than I should have thrown around allowed so it's not really allowed it's really capable right the game tree is restricted because people are incapable of playing moves that are not computable by their computers so so it may be maybe that maybe that refinement of learning would help would help there I mean looks like let's take this long okay I'll take offline excellent okay and now we can tell by the way okay we all that tension other questions other questions can when you look at me look at the commercial this is this is very reminiscent if you want to see what is the set up winning strategies based on that anyone up in a certain tree with this basic basically what's the support right so you could you could be happening rolls over these right two to two - to see you know because of the path that the path or the ones that are that are that are not computable will give you zero right right because there's no support right but if you're if you're if you're integrating the path of the world WWI and you're dirty you're going we can express it to paths that you can actually because it's you can treat the power series you can then Excel exponentiate so that that's so now now you actually now you'll actually have a have a have a have a corresponding that you can you can compute total total total total values of census right beautiful positive it goes I don't know they apply but that sounds great so this is talking out there that that's exactly what I'm trying to do here is and make up something that sounds legit enough that you believe me the hell to it will be supported by it but that you can stick on your actual knowledge of computability and cryptography because mine is woefully inadequate to deal with these sort of systemic problem actually it's actually more okay what about me my not sure about today okay absolutely so let's check after yeah in general I'll be around after everyone who wants to come let's come talk about this stuff okay it's like a very a very simple computer ability model that you can build which is one that we sort of deal with in in the statement which may or may not be of course the accurate at all is maybe maybe the way that we define our world and as we say that the world is that the world and the set of worlds is applied my three things a set of public information I set of secret information to P and a sort of secret information right and you maintain the rule whatever the world is a particularly we say that in all worlds it holds true that if some act something's up some that said element X is in the secret information of a then it is not in the public information okay so if a if a has to see an information that is not in the public information right and the further we say the computable the computable moves that can be played is the intersection of all the possible groups with the public information set so what this means instead of X is in I I be secret then therefore it's not in I public and therefore it's not in this intersection and it's not playable so this is a very simple very rudimentary way to try to restrict these game trees it's probably has nothing to do like a you know maybe when I said this was like universe of composability and get it you know I get an actual security model that corresponds to crypto slapped on it this is probably not it but it gives you a good intuition for what's going on yes that's the question it's public but it is it or private yeah so what is it right right so we'll say the public the public information is known by both parties that's why we're calling it public right and so maybe this isn't accurate to the meaning so for example if we extend this to can't party world on which there are many different play people playing things there's not one public set of information there's a set of information that I have downloaded and there's a set of information that's secret to me that I know that no one else is downloaded but making the local information that is public that I have downloaded is not is not is not that downloaded by someone else right so there's many more complex models you can build far more complex models and that's what we need we need a better model this is a very simple one that we can throw together just to pull out the course or elements of other questions five minutes which I'm pretty pleased because we're pretty much there okay so a really simple example with this very very very simple model which again probably not accurate to the computer science out there but it's accurate enough to give us a layered you can treat that actually corresponds to what really is done on chained in literature so the preimage existence you know you know sort of predicate is like the simplest sort of rudimentary example of what happens right so the game or proposition is as follows there exists a hash in you know the set of lights such that is has privileged H and H naught for some some fixed H naught is known okay so this game has a different game tree depending on whether or not H the particularly you know a little H is known it's in the moment information or is not right so this is the game for this game up there so we'll W in which H naught is in pub then this game is true this game is true right because the premiere says there exists a chance the purpose of this thing then the abundance has no hope for all age not is Hashmi image but because H naught is in the public information he may choose it is in the computable subset so it may be played and so now that the P naught is hatched village Judas is that not decided image purchases fish has been image and this is true right so it's one by people so in a world in which H naught is in the public domain then this proposition is interpreted as true because this is a winning strategy for that composition for the proven however instead H naught is secret right its secrets to the opponent then this will not be true because this step which we previously had is is not to be is not computable it's not possible random may be allowed it's not possible because H naught is not in peace it's not in the public center information so you have to play and no matter what the actual world is right so maybe the rest of the elements we said we might play some H prime or some major private line but no matter what happens there those are gonna be false because of that they only inch only this image not which is secret and there we're not playable there's gonna be the thing that gets us to a true statement at the bottom a truly a true game outcome okay and so normally what this means is that if we start out in this in this world in which H not the secret to vote then this proposition is false but its desired by by the opponent oh may reveal that preimage and in doing so it would change the world that the world would know what managed by my security would go back to this one and it would now be true so we've changed the truth so we started in a world where the game where the thing is false and we added a thing in which the thing is true right and because we can do that off chain and because we can enforce these games on chain this is how we get the scalability of player two solutions wouldn't it be sort of cleaner and easier to think about if you just said Pino is H such that sure that might that might be cleaner yeah absolutely absolutely yeah so this is a very simple thing you like started together because point I want to get across is these games were what happened on to me earlier twos and someone's you'll be able to do the spring rehearsal yet effectively yes your local public information an example of our building and Priya doesn't make the city this may be necessarily true for all participants just the party that actually revealed to absolutely right and that's why so far I've defined the semantics as between two imaginary players of group Republic where you're absolutely right well we need to do to like hit this with the universal composability but you know at that you know epic like formal proof you know for all they are to model is we need to have that we need to have a say you know a distributed system like thank many many people public shared information what what has been published shared to anyone was been publishers only some people and when it's not the publisher aka is private right so absolutely this is lonely and if you think you know it or know a good way to do it or how something knows gonna do it come find you ah what is it useful for so-and-so as we have exactly one minute to go what is it useful for well here is a state channel so the thing that we've been doing all along to come upon state channels and we've thought of as a unique thing is actually simply this expression okay so this is a pre-image reveal stage channel so we imagine that there's a set of hashes which are all secret to the opponent in the beginning and as we progress to your worlds we selectively revealed each patch and by associated a game of the form channel s2 a payout of the form s so that we pay say s coins out to someone we can actually associate money with this game and by selectively revealing these three images we selected they're paid at one collector nomination through the planning so that's a state journal okay we can also do certain or aetherium style change you know so here's our multi sync that we had before there's a multi sing as I'm the day before in a theory of style channel as I claim for this day there exists some obesity and fourtner's does not exist the higher snake such that there's an officer and the state is indeed higher with a higher knots right so there's that here's how the music roll up do you pick that exchange but just remember this this is a roll of chain computability model of care for roll ups are really nice is that it is a chain always makes data available so the computability ball is much easier for any information that's on the main chain because it's always no it can't be in this very great property and make sure it very very very simple graceful elegant distress of an elegant thing because it's nice to learn lastly it's plasma which is God awfully complicated expression somebody and it's the simplest possible construction I think about them but I can tell you the distant deep works is we got a paper that talks more about opposition money with this Allah we got to go thank you very much [Applause]