Abstract
This paper presents a decision procedure for the alternating-time μ-calculus. The algorithm is based on a representation of alternating-time formulas as automata over concurrent game structures. We show that language emptiness of these automata can be checked in exponential time. The complexity of our construction meets the known lower bounds for deciding the satisfiability of the classic μ-calculus. It follows that the satisfiability problem is EXPTIME-complete for the alternating-time μ-calculus.
This work was partly supported by the German Research Foundation (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).
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Schewe, S., Finkbeiner, B. (2006). Satisfiability and Finite Model Property for the Alternating-Time μ-Calculus. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_39
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DOI: https://doi.org/10.1007/11874683_39
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