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arXiv · 1407.5166

The Expressive Power of Epistemic $\mu$-Calculus

Cătălin Dima·Bastien Maubert·Sophie Pinchinat
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Abstract

While the $\mu$-calculus notoriously subsumes Alternating-time Temporal Logic (ATL), we show that the epistemic $\mu$-calculus does not subsume ATL with imperfect information (ATL$_i$) for the synchronous perfect-recall semantics. To prove this we first establish that jumping parity tree automata (JTA), a recently introduced extension of alternating parity tree automata, are expressively equivalent to the epistemic $\mu$-calculus, and this for any knowledge semantics. Using this result we also show that, for bounded-memory semantics, the epistemic $\mu$-calculus is not more expressive than the standard $\mu$-calculus, and that its satisfiability problem is EXPTIME-complete.

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Cătălin Dima, Bastien Maubert, Sophie Pinchinat. 2014-07-19. The Expressive Power of Epistemic $\mu$-Calculus. https://arxiv.org/abs/1407.5166

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