{"title":"Quantitative Automata under Probabilistic Semantics","authors":"K. Chatterjee, T. Henzinger, J. Otop","doi":"10.1145/2933575.2933588","DOIUrl":"https://doi.org/10.1145/2933575.2933588","url":null,"abstract":"Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132591797","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":"Perfect-Information Stochastic Games with Generalized Mean-Payoff Objectives*","authors":"K. Chatterjee, L. Doyen","doi":"10.1145/2933575.2934513","DOIUrl":"https://doi.org/10.1145/2933575.2934513","url":null,"abstract":"Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph are controlled by two adversarial players, and the other transitions are executed probabilistically. We consider such games where the objective is the conjunction of several quantitative objectives (specified as mean-payoff conditions), which we refer to as generalized mean-payoff objectives. The basic decision problem asks for the existence of a finite-memory strategy for a player that ensures the generalized mean-payoff objective be satisfied with a desired probability against all strategies of the opponent. A special case of the decision problem is the almost-sure problem where the desired probability is 1. Previous results presented a semi-decision procedure for ε-approximations of the almost-sure problem. In this work, we show that both the almost-sure problem as well as the general basic decision problem are coNP-complete, significantly improving the previous results. Moreover, we show that in the case of 1-player stochastic games, randomized memoryless strategies are sufficient and the problem can be solved in polynomial time. In contrast, in two-player stochastic games, we show that even with randomized strategies exponential memory is required in general, and present a matching exponential upper bound. We also study the basic decision problem with infinite-memory strategies and present computational complexity results for the problem. Our results are relevant in the synthesis of stochastic reactive systems with multiple quantitative requirements.Categories and Subject Descriptors F.2.2 [Computations on Discrete Structures]","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131178804","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":"Order-Invariance of Two-Variable Logic is Decidable","authors":"T. Zeume, Frederik Harwath","doi":"10.1145/2933575.2933594","DOIUrl":"https://doi.org/10.1145/2933575.2933594","url":null,"abstract":"It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two first-order variables (ESO2) on structures with two linear orders and one induced successor. We also show that finite satisfiability is decidable on structures with two successors and one induced linear order. In both cases, so far only decidability for monadic ESO2 has been known. In addition, the finite satisfiability problem for ESO2 on structures with one linear order and its induced successor relation is shown to be decidable in non-deterministic exponential time.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133916116","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}
Federico Olmedo, Benjamin Lucien Kaminski, J. Katoen, C. Matheja
{"title":"Reasoning about Recursive Probabilistic Programs*","authors":"Federico Olmedo, Benjamin Lucien Kaminski, J. Katoen, C. Matheja","doi":"10.1145/2933575.2935317","DOIUrl":"https://doi.org/10.1145/2933575.2935317","url":null,"abstract":"This paper presents a wp–style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one– and two–sided bounds for such expectations, and show the soundness of our wp–calculus with respect to a probabilistic pushdown automaton semantics. We also give a wp–style calculus for obtaining bounds on the expected runtime of recursive programs that can be used to determine the (possibly infinite) time until termination of such programs.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125263094","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":"Trace semantics for polymorphic references*","authors":"Guilhem Jaber, N. Tzevelekos","doi":"10.1145/2933575.2934509","DOIUrl":"https://doi.org/10.1145/2933575.2934509","url":null,"abstract":"We introduce a trace semantics for a call-by-value language with full polymorphism and higher-order references. This is an operational game semantics model based on a nominal interpretation of parametricity whereby polymorphic values are abstracted with special kinds of names. The use of polymorphic references leads to violations of parametricity which we counter by closely recoding the disclosure of typing information in the semantics. We prove the model sound for the full language and strengthen our result to full abstraction for a large fragment where polymorphic references obey specific inhabitation conditions.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115792094","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}
F. Bonchi, F. Gadducci, A. Kissinger, P. Sobocinski, F. Zanasi
{"title":"Rewriting modulo symmetric monoidal structure","authors":"F. Bonchi, F. Gadducci, A. Kissinger, P. Sobocinski, F. Zanasi","doi":"10.1145/2933575.2935316","DOIUrl":"https://doi.org/10.1145/2933575.2935316","url":null,"abstract":"String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114147585","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":"The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems","authors":"L. Barto, M. Pinsker","doi":"10.1145/2933575.2934544","DOIUrl":"https://doi.org/10.1145/2933575.2934544","url":null,"abstract":"We prove that an ω-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that this happens if and only if its polymorphism clone does not contain operations α,β, s satisfying the identity αs(x, y, x, z, y, z) ≈ βs(y, x, z, x, z, y).This establishes an algebraic criterion equivalent to the conjectured borderline between P and NP-complete CSPs over reducts of finitely bounded homogenous structures, and accomplishes one of the steps of a proposed strategy for reducing the infinite domain CSP dichotomy conjecture to the finite case.Our theorem is also of independent mathematical interest, characterizing a topological property of any ω-categorical core structure (the existence of a continuous homomorphism of a stabilizer of its polymorphism clone to the projections) in purely algebraic terms (the failure of an identity as above).","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"159 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125937102","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}
M. Atig, D. Chistikov, Piotr Hofman, K. Kumar, Prakash Saivasan, Georg Zetzsche
{"title":"The complexity of regular abstractions of one-counter languages","authors":"M. Atig, D. Chistikov, Piotr Hofman, K. Kumar, Prakash Saivasan, Georg Zetzsche","doi":"10.1145/2933575.2934561","DOIUrl":"https://doi.org/10.1145/2933575.2934561","url":null,"abstract":"We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) $mathcal{A}$, construct a nondeterministic finite automaton (NFA) $mathcal{B}$ that recognizes an abstraction of the language $mathcal{L}left( mathcal{A} right)$: its (1) downward closure, (2) upward closure, or (3) Parikh image. For the Parikh image over a fixed alphabet and for the upward and downward closures, we find polynomial-time algorithms that compute such an NFA. For the Parikh image with the alphabet as part of the input, we find a quasi-polynomial time algorithm and prove a completeness result: we construct a sequence of OCA that admits a polynomial-time algorithm iff there is one for all OCA. For all three abstractions, it was previously unknown whether appropriate NFA of sub-exponential size exist.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133929047","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}
K. Chatterjee, W. Dvořák, M. Henzinger, Veronika Loitzenbauer
{"title":"Model and Objective Separation with Conditional Lower Bounds: Disjunction is Harder than Conjunction *","authors":"K. Chatterjee, W. Dvořák, M. Henzinger, Veronika Loitzenbauer","doi":"10.1145/2933575.2935304","DOIUrl":"https://doi.org/10.1145/2933575.2935304","url":null,"abstract":"Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to several fundamental ω-regular objectives, e.g., Rabin and Streett objectives. For many of these problems the best-known upper bounds are quadratic or cubic, yet no super-linear lower bounds are known. In this work our contributions are two-fold: First, we present several improved algorithms, and second, we present the first conditional super-linear lower bounds based on widely believed assumptions about the complexity of CNF-SAT and combinatorial Boolean matrix multiplication. A separation result for two models with respect to an objective means a conditional lower bound for one model that is strictly higher than the existing upper bound for the other model, and similarly for two objectives with respect to a model. Our results establish the following separation results: (1) A separation of models (graphs and MDPs) for disjunctive queries of reachability and Büchi objectives. (2) Two kinds of separations of objectives, both for graphs and MDPs, namely, (2a) the separation of dual objectives such as Streett/Rabin objectives, and (2b) the separation of conjunction and disjunction of multiple objectives of the same type such as safety, Büchi, and coBüchi. In summary, our results establish the first model and objective separation results for graphs and MDPs for various classical ω-regular objectives. Quite strikingly, we establish conditional lower bounds for the disjunction of objectives that are strictly higher than the existing upper bounds for the conjunction of the same objectives.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"7 Suppl 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126330546","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":"Winning Cores in Parity Games","authors":"Steen Vester","doi":"10.1145/2933575.2933589","DOIUrl":"https://doi.org/10.1145/2933575.2933589","url":null,"abstract":"We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number properties about winning cores which are interesting in their own right. In particular, we show that the winning core and the winning region for a player in a parity game are equivalently empty. Moreover, the winning core contains all fatal attractors but is not necessarily a dominion itself. Experimental results are very positive both with respect to quality of approximation and running time. It outperforms existing state-of-the-art algorithms significantly on most benchmarks.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126794321","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}