{"title":"Bounded Game-Theoretic Semantics for Modal Mu-Calculus and Some Variants","authors":"L. Hella, Antti Kuusisto, Raine Rönnholm","doi":"10.4204/EPTCS.326.6","DOIUrl":"https://doi.org/10.4204/EPTCS.326.6","url":null,"abstract":"We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133623442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Í. Í. Romeo, L. Mangeruca, T. Villa, A. Sangiovanni-Vincentelli
{"title":"The Quotient in Preorder Theories","authors":"Í. Í. Romeo, L. Mangeruca, T. Villa, A. Sangiovanni-Vincentelli","doi":"10.4204/EPTCS.326.14","DOIUrl":"https://doi.org/10.4204/EPTCS.326.14","url":null,"abstract":"Seeking the largest solution to an expression of the form A x <= B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128667597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Symbolic Execution + Model Counting + Entropy Maximization = Automatic Search Synthesis","authors":"M. Downing, A. Molavi, Lucas Bang","doi":"10.4204/EPTCS.326.4","DOIUrl":"https://doi.org/10.4204/EPTCS.326.4","url":null,"abstract":"We present a method of automatically synthesizing steps to solve search problems. Given a specification of a search problem, our approach uses symbolic execution to analyze the specification in order to extract a set of constraints which model the problem. These constraints are used in a process called model counting, which is leveraged to compute probability distributions relating search steps to predicates about an unknown target. The probability distribution functions determine an information gain objective function based on Shannon entropy, which, when maximized, yields the next optimal step of the search. We prove that our algorithm converges to a correct solution, and discuss computational complexity issues. We implemented a domain specific language in which to write search problem specifications, enabling our static analysis phase. Our experiments demonstrate the effectiveness of our approach on a set of search problem case studies inspired by the domains of software security, computational geometry, AI for games, and user preference ranking.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131339186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Game Theoretical Semantics for Logics of Nonsense","authors":"Can Başkent","doi":"10.4204/EPTCS.326.5","DOIUrl":"https://doi.org/10.4204/EPTCS.326.5","url":null,"abstract":"Logics of non-sense allow a third truth value to express propositions that are emph{nonsense}. These logics are ideal formalisms to understand how errors are handled in programs and how they propagate throughout the programs once they appear. In this paper, we give a Hintikkan game semantics for logics of non-sense and prove its correctness. We also discuss how a known solution method in game theory, the iterated elimination of strictly dominated strategies, relates to semantic games for logics of nonsense. Finally, we extend the logics of nonsense only by means of semantic games, developing a new logic of nonsense, and propose a new game semantics for Priest's Logic of Paradox.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121475649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrew M. Wells, Morteza Lahijanian, L. Kavraki, Moshe Y. Vardi
{"title":"LTLf Synthesis on Probabilistic Systems","authors":"Andrew M. Wells, Morteza Lahijanian, L. Kavraki, Moshe Y. Vardi","doi":"10.4204/EPTCS.326.11","DOIUrl":"https://doi.org/10.4204/EPTCS.326.11","url":null,"abstract":"Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122761965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"LTLf Synthesis under Partial Observability: From Theory to Practice","authors":"L. M. Tabajara, Moshe Y. Vardi","doi":"10.4204/EPTCS.326.1","DOIUrl":"https://doi.org/10.4204/EPTCS.326.1","url":null,"abstract":"LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics (LTLf) allows for significantly simpler implementations in practice. With the conceptual simplicity of LTLf, it becomes possible to explore extensions such as partial observability in practice for the first time. Previous work has analyzed the problem of LTLf synthesis under partial observability theoretically and suggested two possible algorithms, one with 3EXPTIME and another with 2EXPTIME complexity. In this work, we first prove a complexity lower bound conjectured in earlier work. Then, we complement the theoretical analysis by showing how the two algorithms can be integrated in practice into an established framework for LTLf synthesis. We furthermore identify a third, MSO-based, approach enabled by this framework. Our experimental evaluation reveals very different results from what the theory seems to suggest, with the 3EXPTIME algorithm often outperforming the 2EXPTIME approach. Furthermore, as long as it is able to overcome an initial memory bottleneck, the MSO-based approach can often outperforms the others.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124863007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Canonicity in GFG and Transition-Based Automata","authors":"Bader Abu Radi, O. Kupferman","doi":"10.4204/EPTCS.326.13","DOIUrl":"https://doi.org/10.4204/EPTCS.326.13","url":null,"abstract":"Minimization of deterministic automata on finite words results in a {em canonical/} automaton. For deterministic automata on infinite words, no canonical minimal automaton exists, and a language may have different minimal deterministic Buchi (DBW) or co-Buchi (DCW) automata. In recent years, researchers have studied {em good-for-games/} (GFG) automata -- nondeterministic automata that can resolve their nondeterministic choices in a way that only depends on the past. Several applications of automata in formal methods, most notably synthesis, that are traditionally based on deterministic automata, can instead be based on GFG automata. The {em minimization/} problem for DBW and DCW is NP-complete, and it stays NP-complete for GFG Buchi and co-Buchi automata. On the other hand, minimization of GFG co-Buchi automata with {em transition-based/} acceptance (GFG-tNCWs) can be solved in polynomial time. In these automata, acceptance is defined by a set $alpha$ of transitions, and a run is accepting if it traverses transitions in $alpha$ only finitely often. This raises the question of canonicity of minimal deterministic and GFG automata with transition-based acceptance. In this paper we study this problem. We start with GFG-tNCWs and show that the safe components (that is, these obtained by restricting the transitions to these not in $alpha$) of all minimal GFG-tNCWs are isomorphic, and that by saturating the automaton with transitions in $alpha$ we get isomorphism among all minimal GFG-tNCWs. Thus, a canonical form for minimal GFG-tNCWs can be obtained in polynomial time. We continue to DCWs with transition-based acceptance (tDCWs), and their dual tDBWs. We show that here, while no canonical form for minimal automata exists, restricting attention to the safe components is useful, and implies that the only minimal tDCWs that have no canonical form are these for which the transition to the GFG model results in strictly smaller automaton, which do have a canonical minimal form.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"55 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128359016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jan Křetínský, Emanuel Ramneantu, Alexander Slivinskiy, Maximilian Weininger
{"title":"Comparison of Algorithms for Simple Stochastic Games (Full Version)","authors":"Jan Křetínský, Emanuel Ramneantu, Alexander Slivinskiy, Maximilian Weininger","doi":"10.4204/EPTCS.326.9","DOIUrl":"https://doi.org/10.4204/EPTCS.326.9","url":null,"abstract":"Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms -- value iteration, strategy iteration and quadratic programming -- both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISM-games 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116014517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Power of Unambiguity in Büchi Complementation","authors":"Yong Li, Moshe Y. Vardi, Lijun Zhang","doi":"10.4204/EPTCS.326.12","DOIUrl":"https://doi.org/10.4204/EPTCS.326.12","url":null,"abstract":"In this work, we exploit the power of unambiguity for the complementation problem of Buchi automata by utilizing reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor. Given a Buchi automaton with n states and a finite degree of ambiguity, we show that the number of states in the complementary Buchi automaton constructed by the classical Rank-based and Slice-based complementation constructions can be improved, respectively, to $2^{mathcal{O}(n)}$ from $2^{mathcal{O}( n log n)}$ and to $mathcal{O}(4^n)$ from $mathcal{O}( (3n)^n)$, based on reduced run DAGs. To the best of our knowledge, the improved complexity is exponentially better than best known result of $mathcal{O}(5^n)$ in [21] for complementing Buchi automata with a finite degree of ambiguity.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123574930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Bérard, B. Bollig, P. Bouyer, Matthias Függer, N. Sznajder
{"title":"Synthesis in Presence of Dynamic Links","authors":"B. Bérard, B. Bollig, P. Bouyer, Matthias Függer, N. Sznajder","doi":"10.4204/EPTCS.326.3","DOIUrl":"https://doi.org/10.4204/EPTCS.326.3","url":null,"abstract":"The problem of distributed synthesis is to automatically generate a distributed algorithm, given a target communication network and a specification of the algorithm's correct behavior. Previous work has focused on static networks with an apriori fixed message size. This approach has two shortcomings: Recent work in distributed computing is shifting towards dynamically changing communication networks rather than static ones, and an important class of distributed algorithms are so-called full-information protocols, where nodes piggy-pack previously received messages onto current messages. In this work we consider the synthesis problem for a system of two nodes communicating in rounds over a dynamic link whose message size is not bounded. Given a network model, i.e., a set of link directions, in each round of the execution, the adversary choses a link from the network model, restricted only by the specification, and delivers messages according to the current link's directions. Motivated by communication buses with direct acknowledge mechanisms we further assume that nodes are aware of which messages have been delivered. We show that the synthesis problem is decidable for a network model if and only if it does not contain the empty link that dismisses both nodes' messages.","PeriodicalId":104855,"journal":{"name":"International Symposium on Games, Automata, Logics and Formal Verification","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115098382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}