289 research outputs found

    Formats of Winning Strategies for Six Types of Pushdown Games

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    The solution of parity games over pushdown graphs (Walukiewicz '96) was the first step towards an effective theory of infinite-state games. It was shown that winning strategies for pushdown games can be implemented again as pushdown automata. We continue this study and investigate the connection between game presentations and winning strategies in altogether six cases of game arenas, among them realtime pushdown systems, visibly pushdown systems, and counter systems. In four cases we show by a uniform proof method that we obtain strategies implementable by the same type of pushdown machine as given in the game arena. We prove that for the two remaining cases this correspondence fails. In the conclusion we address the question of an abstract criterion that explains the results

    Regular Methods for Operator Precedence Languages

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    The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the ultimate verification problem. Operator precedence grammars, automata, and logics have been investigated and used, for example, to verify programs with arithmetic expressions and exceptions (both of which are deterministic pushdown but lie outside the scope of the visibly pushdown languages). In this paper, we complete the picture and give, for the first time, an algebraic characterization of the class of OPLs in the form of a syntactic congruence that has finitely many equivalence classes exactly for the operator precedence languages. This is a generalization of the celebrated Myhill-Nerode theorem for the regular languages to OPLs. As one of the consequences, we show that universality and language inclusion for nondeterministic operator precedence automata can be solved by an antichain algorithm. Antichain algorithms avoid determinization and complementation through an explicit subset construction, by leveraging a quasi-order on words, which allows the pruning of the search space for counterexample words without sacrificing completeness. Antichain algorithms can be implemented symbolically, and these implementations are today the best-performing algorithms in practice for the inclusion of finite automata. We give a generic construction of the quasi-order needed for antichain algorithms from a finite syntactic congruence. This yields the first antichain algorithm for OPLs, an algorithm that solves the ExpTime-hard language inclusion problem for OPLs in exponential time

    Model counting for reactive systems

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    Model counting is the problem of computing the number of solutions for a logical formula. In the last few years, it has been primarily studied for propositional logic, and has been shown to be useful in many applications. In planning, for example, propositional model counting has been used to compute the robustness of a plan in an incomplete domain. In information-flow control, model counting has been applied to measure the amount of information leaked by a security-critical system. In this thesis, we introduce the model counting problem for linear-time properties, and show its applications in formal verification. In the same way propositional model counting generalizes the satisfiability problem for propositional logic, counting models for linear-time properties generalizes the emptiness problem for languages over infinite words to one that asks for the number of words in a language. The model counting problem, thus, provides a foundation for quantitative extensions of model checking, where not only the existence of computations that violate the specification is determined, but also the number of such violations. We solve the model counting problem for the prominent class of omega-regular properties. We present algorithms for solving the problem for different classes of properties, and show the advantages of our algorithms in comparison to indirect approaches based on encodings into propositional logic. We further show how model counting can be used for solving a variety of quantitative problems in formal verification, including probabilistic model checking, quantitative information-flow in security-critical systems, and the synthesis of approximate implementations for reactive systems.Das ModellzĂ€hlproblem fragt nach der Anzahl der Lösungen einer logischen Formel, und wurde in den letzten Jahren hauptsĂ€chlich fĂŒr Aussagenlogik untersucht. Das ZĂ€hlen von Modellen aussagenlogischer Formeln hat sich in vielen Anwendungen als nĂŒtzlich erwiesen. Im Bereich der kĂŒnstlichen Intelligenz wurde das ZĂ€hlen von Modellen beispielsweise verwendet, um die Robustheit eines Plans in einem unvollstĂ€ndigen Weltmodell zu bewerten. Das ZĂ€hlen von Modellen kann auch verwendet werden, um in sicherheitskritischen Systemen die Menge an enthĂŒllten vertraulichen Daten zu messen. Diese Dissertation stellt das ModellzĂ€hlproblem fĂŒr Linearzeiteigenschaften vor, und untersucht dessen Rolle in der Welt der formalen Verifikation. Das ZĂ€hlen von Modellen fĂŒr Linearzeiteigenschaften fĂŒhrt zu neuen quantitativen Erweiterungen klassischer Verifikationsprobleme, bei denen nicht nur die Existenz eines Fehlers in einem System zu ĂŒberprĂŒfen ist, sondern auch die Anzahl solcher Fehler. Wir prĂ€sentieren Algorithmen zur Lösung des ModellzĂ€hlproblems fĂŒr verschiedene Klassen von Linearzeiteigenschaften und zeigen die Vorteile unserer Algorithmen im Vergleich zu indirekten AnsĂ€tzen, die auf Kodierungen der untersuchten Probleme in Aussagenlogik basieren. DarĂŒberhinaus zeigen wir wie das ZĂ€hlen von Modellen zur Lösung einer Vielzahl quantitativer Probleme in der formalen Verifikation verwendet werden kann. Dies beinhaltet unter anderem die Analyse probabilistischer Modelle, die Kontrolle quantitativen Informationsflusses in sicherheitskritischen Systemen, und die Synthese von approximativen Implementierungen fĂŒr reaktive Systeme

    Acta Cybernetica : Volume 17. Number 4.

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    Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

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    In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio

    26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

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    Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft fĂŒr Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintĂ€gigen Workshop mit eingeladenen VortrĂ€gen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft fĂŒr Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jĂ€hrliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe ZuverlĂ€ssige Systeme des Instituts fĂŒr Informatik an der Christian-Albrechts-UniversitĂ€t Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei NeumĂŒnster. WĂ€hrend des Tre↔ens wird ein Workshop fĂŒr alle Interessierten statt finden. In Tannenfelde werden ‱ Christoph Löding (Aachen) ‱ TomĂĄs Masopust (Dresden) ‱ Henning Schnoor (Kiel) ‱ Nicole Schweikardt (Berlin) ‱ Georg Zetzsche (Paris) eingeladene VortrĂ€ge zu ihrer aktuellen Arbeit halten. DarĂŒber hinaus werden 26 VortrĂ€ge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthĂ€lt Kurzfassungen aller BeitrĂ€ge. Wir danken der Gesellschaft fĂŒr Informatik, der Christian-Albrechts-UniversitĂ€t zu Kiel und dem Tagungshotel Tannenfelde fĂŒr die UnterstĂŒtzung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

    Lukasiewicz mu-Calculus

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    We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations

    Modal logics on rational Kripke structures

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    This dissertation is a contribution to the study of infinite graphs which can be presented in a finitary way. In particular, the class of rational graphs is studied. The vertices of a rational graph are labeled by a regular language in some finite alphabet and the set of edges of a rational graph is a rational relation on that language. While the first-order logics of these graphs are generally not decidable, the basic modal and tense logics are. A survey on the class of rational graphs is done, whereafter rational Kripke models are studied. These models have rational graphs as underlying frames and are equipped with rational valuations. A rational valuation assigns a regular language to each propositional variable. I investigate modal languages with decidable model checking on rational Kripke models. This leads me to consider regularity preserving relations to see if the class can be generalised even further. Then the concept of a graph being rationally presentable is examined - this is analogous to a graph being automatically presentable. Furthermore, some model theoretic properties of rational Kripke models are examined. In particular, bisimulation equivalences between rational Kripke models are studied. I study three subclasses of rational Kripke models. I give a summary of the results that have been obtained for these classes, look at examples (and non-examples in the case of automatic Kripke frames) and of particular interest is finding extensions of the basic tense logic with decidable model checking on these subclasses. An extension of rational Kripke models is considered next: omega-rational Kripke models. Some of their properties are examined, and again I am particularly interested in finding modal languages with decidable model checking on these classes. Finally I discuss some applications, for example bounded model checking on rational Kripke models, and mention possible directions for further research

    Algorithms for Game Metrics

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    Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative {\mu}-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n^4) for both turn-based games and MDPs; improving the previously best known O(n^9\cdot log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(|G|^O(|G|^5)) time complexity, improving the previously known reduction, which yielded O(|G|^O(|G|^7)) time complexity. These algorithms can be iterated to approximate the metrics using binary search.Comment: 27 pages. Full version of the paper accepted at FSTTCS 200
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