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Size-Change Termination and Satisfiability for Linear-Time Temporal Logics

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Frontiers of Combining Systems (FroCoS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6989))

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Abstract

In the automata-theoretic framework, finite-state automata are used as a machine model to capture the operational content of temporal logics. Decision problems like satisfiability, subsumption, equivalence, etc. then translate into questions on automata like emptiness, inclusion, language equivalence, etc. Linear-time temporal logics like LTL, PSL and the linear-time μ-calculus have relatively simple translations into alternating parity automata, and this automaton model is closed under all Boolean operations with very simple constructions. Thus, the typical decision problems for such linear-time temporal logics reduce relatively simply to the emptiness problem for alternating parity automata. In this paper we present a method for decision this emptiness problem without going through intermediate automaton models like nondeterministic ones. The method is a direct adaptation of the size-change termination principle which was orgininally used to decide termination of abstract functional programs.

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Authors and Affiliations

  1. School of Electr. Eng. and Computer Science, University of Kassel, Germany

    Martin Lange

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  1. Martin Lange
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Editors and Affiliations

  1. University of Iowa, USA

    Cesare Tinelli

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

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Lange, M. (2011). Size-Change Termination and Satisfiability for Linear-Time Temporal Logics. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-24364-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24363-9

  • Online ISBN: 978-3-642-24364-6

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