2012 27th Annual IEEE Symposium on Logic in Computer Science最新文献

{"title":"Better Abstractions for Timed Automata","authors":"F. Herbreteau, B. Srivathsan, I. Walukiewicz","doi":"10.1109/LICS.2012.48","DOIUrl":"https://doi.org/10.1109/LICS.2012.48","url":null,"abstract":"We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. These abstractions preserve underlying simulation relations on the state space of the automaton. For both effectiveness and efficiency reasons, they are parameterized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of the automaton. We consider the aLU abstraction defined by Behrmann et al. Since this abstraction can potentially yield non-convex sets, it has not been used in implementations. We prove that aLU abstraction is the coarsest abstraction with respect to LU-bounds that is sound and complete for reachability. We also provide an efficient technique to use the aLU abstraction to solve the reachability problem.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"1271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116888022","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":"Decidable Problems for Probabilistic Automata on Infinite Words","authors":"K. Chatterjee, M. Tracol","doi":"10.1109/LICS.2012.29","DOIUrl":"https://doi.org/10.1109/LICS.2012.29","url":null,"abstract":"We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether words are accepted with probability arbitrarily close to 1. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape (regular) words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions. For most decidable problems we show an optimal PSPACE-complete complexity bound.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114156449","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":"Partial-Observation Stochastic Games: How to Win When Belief Fails","authors":"K. Chatterjee, L. Doyen","doi":"10.1109/LICS.2012.28","DOIUrl":"https://doi.org/10.1109/LICS.2012.28","url":null,"abstract":"We consider two-player stochastic games played on finite graphs with reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1), or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, the players (a) may not be allowed to use randomization (pure strategies), or (b) may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) may use full randomization. Our main results for pure strategies are as follows. (1) For one-sided games with player 1 having partial observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete. (2) For one-sided games with player 2 having partial observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibits serious flaws in previous results of the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122804119","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":"Deciding the Value 1 Problem for Probabilistic Leaktight Automata","authors":"Nathanaël Fijalkow, H. Gimbert, Edon Kelmendi, Y. Oualhadj","doi":"10.1109/LICS.2012.40","DOIUrl":"https://doi.org/10.1109/LICS.2012.40","url":null,"abstract":"The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton, are there words accepted with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviors of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121552304","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":"Short Propositional Refutations for Dense Random 3CNF Formulas","authors":"Sebastian Müller, Iddo Tzameret","doi":"10.1109/LICS.2012.60","DOIUrl":"https://doi.org/10.1109/LICS.2012.60","url":null,"abstract":"Random 3CNF formulas constitute an important distribution for measuring the average-case behavior of propositional proof systems. Lower bounds for random 3CNF refutations in many propositional proof systems are known. Most notable are the exponential-size resolution refutation lower bounds for random 3CNF formulas with Ω(n1.5-ε) clauses (Chvatal and Szemeredi [13], Ben-Sasson and Wigderson [9]). On the other hand, the only known non-trivial upper bound on the size of random 3CNF refutations in a non-abstract propositional proof system is for resolution with Ω(n2/ log n) clauses, shown by Beame et al. [5]. In this paper we show that already standard propositional proof systems, within the hierarchy of Frege proofs, admit short refutations for random 3CNF formulas, for sufficiently large clause-to-variable ratio. Specifically, we demonstrate polynomialsize propositional refutations whose lines are TC0 formulas (i.e., TC0-Frege proofs) for random 3CNF formulas with n variables and Ω(n1.4) clauses. The idea is based on demonstrating efficient propositional correctness proofs of the random 3CNF unsatisfiability witnesses given by Feige, Kim and Ofek [19]. Since the soundness of these witnesses is verified using spectral techniques, we develop an appropriate way to reason about eigenvectors in propositional systems. To carry out the full argument we work inside weak formal systems of arithmetic and use a general translation scheme to propositional proofs.","PeriodicalId":407972,"journal":{"name":"2012 27th Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128710739","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}