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arXiv · 1710.08996

Permutation Games for the Weakly Aconjunctive $\mu$-Calculus

Daniel Hausmann·Lutz Schröder·Hans-Peter Deifel
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Abstract

We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the $\mu$-calculus. To this end we devise a method that determinizes limit-deterministic parity automata of size $n$ with $k$ priorities through limit-deterministic B\"uchi automata to deterministic parity automata of size $\mathcal{O}((nk)!)$ and with $\mathcal{O}(nk)$ priorities. The construction relies on limit-determinism to avoid the full complexity of the Safra/Piterman-construction by using partial permutations of states in place of Safra-Trees. By showing that limit-deterministic parity automata can be used to recognize unsuccessful branches in pre-tableaux for the weakly aconjunctive $\mu$-calculus, we obtain satisfiability games of size $\mathcal{O}((nk)!)$ with $\mathcal{O}(nk)$ priorities for weakly aconjunctive input formulas of size $n$ and alternation-depth $k$. A prototypical implementation that employs a tableau-based global caching algorithm to solve these games on-the-fly shows promising initial results.

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Daniel Hausmann, Lutz Schröder, Hans-Peter Deifel. 2017-10-24. Permutation Games for the Weakly Aconjunctive $\mu$-Calculus. https://arxiv.org/abs/1710.08996

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