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Reasoning about the past with two-way automata

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Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

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Abstract

The Μ-calculus can be viewed as essentially the “ultimate” program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the Μ-calculus is EXPTIME-complete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the Μ-calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on infinite trees.

Supported in part by NSF grants CCR-9628400 and CCR-9700061, and by a grant from the Intel Corporation. URL: http://www.cs.rice.edu/~vardi.

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Authors and Affiliations

  1. Department of Computer Science, Rice University, 77005-1892, Houston, TX, USA

    Moshe Y. Vardi

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  1. Moshe Y. Vardi
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Kim G. Larsen Sven Skyum Glynn Winskel

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© 1998 Springer-Verlag Berlin Heidelberg

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Vardi, M.Y. (1998). Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055090

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  • DOI: https://doi.org/10.1007/BFb0055090

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  • Online ISBN: 978-3-540-68681-1

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