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.
@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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