1,015 research outputs found

    An Effective Extension of the Wagner Hierarchy to Blind Counter Automata

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    International audienceThe extension of the Wagner hierarchy to blind counter automata accepting infinite words with a Muller acceptance condition is effective. We determine precisely this hierarchy

    Wadge Degrees of ω\omega-Languages of Petri Nets

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    We prove that ω\omega-languages of (non-deterministic) Petri nets and ω\omega-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω\omega-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω\omega-languages of (non-deterministic) Turing machines which also form the class of effective analytic sets. In particular, for each non-null recursive ordinal α<ω_1CK\alpha < \omega\_1^{{\rm CK}} there exist some Σ0_α{\bf \Sigma}^0\_\alpha-complete and some Π0_α{\bf \Pi}^0\_\alpha-complete ω\omega-languages of Petri nets, and the supremum of the set of Borel ranks of ω\omega-languages of Petri nets is the ordinal γ_21\gamma\_2^1, which is strictly greater than the first non-recursive ordinal ω_1CK\omega\_1^{{\rm CK}}. We also prove that there are some Σ_11{\bf \Sigma}\_1^1-complete, hence non-Borel, ω\omega-languages of Petri nets, and that it is consistent with ZFC that there exist some ω\omega-languages of Petri nets which are neither Borel nor Σ_11{\bf \Sigma}\_1^1-complete. This answers the question of the topological complexity of ω\omega-languages of (non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326

    Borel Ranks and Wadge Degrees of Context Free Omega Languages

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    We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power than Turing machines equipped with a B\"uchi acceptance condition. In particular, for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete omega context free languages accepted by 1-counter B\"uchi automata, and the supremum of the set of Borel ranks of context free omega languages is the ordinal gamma^1_2 which is strictly greater than the first non recursive ordinal. This very surprising result gives answers to questions of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621]

    Language Design for Reactive Systems: On Modal Models, Time, and Object Orientation in Lingua Franca and SCCharts

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    Reactive systems play a crucial role in the embedded domain. They continuously interact with their environment, handle concurrent operations, and are commonly expected to provide deterministic behavior to enable application in safety-critical systems. In this context, language design is a key aspect, since carefully tailored language constructs can aid in addressing the challenges faced in this domain, as illustrated by the various concurrency models that prevent the known pitfalls of regular threads. Today, many languages exist in this domain and often provide unique characteristics that make them specifically fit for certain use cases. This thesis evolves around two distinctive languages: the actor-oriented polyglot coordination language Lingua Franca and the synchronous statecharts dialect SCCharts. While they take different approaches in providing reactive modeling capabilities, they share clear similarities in their semantics and complement each other in design principles. This thesis analyzes and compares key design aspects in the context of these two languages. For three particularly relevant concepts, it provides and evaluates lean and seamless language extensions that are carefully aligned with the fundamental principles of the underlying language. Specifically, Lingua Franca is extended toward coordinating modal behavior, while SCCharts receives a timed automaton notation with an efficient execution model using dynamic ticks and an extension toward the object-oriented modeling paradigm

    Logic and Automata

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    Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field
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