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DOI: 10.4230/LIPIcs.CONCUR.2016.34

Global Caching for the Alternation-free µ-Calculus

Authors: Daniel Hausmann, Lutz Schröder, and Christoph Egger

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract

We present a sound, complete, and optimal single-pass tableau algorithm for the alternation-free mu-calculus. The algorithm supports global caching with intermediate propagation and runs in time 2^O(n). In game-theoretic terms, our algorithm integrates the steps for constructing and solving the Büchi game arising from the input tableau into a single procedure; this is done on-the-fly, i.e. may terminate before the game has been fully constructed. This suggests a slogan to the effect that global caching = game solving on-the-fly. A prototypical implementation shows promising initial results.

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Daniel Hausmann, Lutz Schröder, and Christoph Egger. Global Caching for the Alternation-free µ-Calculus. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hausmann_et_al:LIPIcs.CONCUR.2016.34,
  author =	{Hausmann, Daniel and Schr\"{o}der, Lutz and Egger, Christoph},
  title =	{{Global Caching for the Alternation-free µ-Calculus}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.34},
  URN =		{urn:nbn:de:0030-drops-61724},
  doi =		{10.4230/LIPIcs.CONCUR.2016.34},
  annote =	{Keywords: modal logic, fixpoint logic, satisfiability, global caching, coalgebraic logic}
}

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Global Caching for the Alternation-free µ-Calculus

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