7,009 research outputs found

    Finitary languages

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    The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata

    The omega-inequality problem for concatenation hierarchies of star-free languages

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    The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing-Th\'erien hierarchy

    There Exist some Omega-Powers of Any Borel Rank

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    Omega-powers of finitary languages are languages of infinite words (omega-languages) in the form V^omega, where V is a finitary language over a finite alphabet X. They appear very naturally in the characterizaton of regular or context-free omega-languages. Since the set of infinite words over a finite alphabet X can be equipped with the usual Cantor topology, the question of the topological complexity of omega-powers of finitary languages naturally arises and has been posed by Niwinski (1990), Simonnet (1992) and Staiger (1997). It has been recently proved that for each integer n > 0, there exist some omega-powers of context free languages which are Pi^0_n-complete Borel sets, that there exists a context free language L such that L^omega is analytic but not Borel, and that there exists a finitary language V such that V^omega is a Borel set of infinite rank. But it was still unknown which could be the possible infinite Borel ranks of omega-powers. We fill this gap here, proving the following very surprising result which shows that omega-powers exhibit a great topological complexity: for each non-null countable ordinal alpha, there exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete omega-powers.Comment: To appear in the Proceedings of the 16th EACSL Annual Conference on Computer Science and Logic, CSL 2007, Lausanne, Switzerland, September 11-15, 2007, Lecture Notes in Computer Science, (c) Springer, 200

    The peculiar horizontal branch morphology of the Galactic globular clusters NGC 6388 and NGC 6441: new insights from UV observations

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    Context. In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441. Aims. We investigate the properties of their anomalous horizontal branches in different photometric planes in order to shed light on the nature of the physical mechanism(s) responsible for the existence of an extended blue tail and of a slope in the horizontal branch, visible in all the color-magnitude diagrams. Methods. New photometric data have been collected and carefully reduced. Empirical data have been compared with updated stellar models of low-mass, metal-rich, He-burning structures, transformed to the observational plane with appropriate model atmospheres. Results. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot horizontal branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and Omega Cen. We briefly review the theoretical scenarios that have been suggested for interpreting this observational feature. We also investigate the tilted horizontal branch morphology and provide further evidence that supports early suggestions that this feature cannot be interpreted as an effect of differential reddening. We show that a possible solution of the puzzle is to assume that a small fraction - ranging between 10-20% - of the stellar population in the two clusters is strongly helium-enriched (Y ~ 0.40 in NGC 6388 and Y ~ 0.35 in NGC 6441). The occurrence of a spread in the He abundance between the canonical value (Y ~ 0.26) and the quoted upper limits can significantly help in explaining the "whole" morphology of the horizontal branch and the pulsational properties of the variable stars in the target clusters

    Acta Cybernetica : Volume 17. Number 4.

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    A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

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    Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for PITL with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs of equally expressive logics with nonelementary computational complexity, our semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning
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