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arXiv · 1408.6477

Tree games with regular objectives

Marcin Przybyłko
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Abstract

We study tree games developed recently by Matteo Mio as a game interpretation of the probabilistic $\mu$-calculus. With expressive power comes complexity. Mio showed that tree games are able to encode Blackwell games and, consequently, are not determined under deterministic strategies. We show that non-stochastic tree games with objectives recognisable by so-called game automata are determined under deterministic, finite memory strategies. Moreover, we give an elementary algorithmic procedure which, for an arbitrary regular language L and a finite non-stochastic tree game with a winning objective L decides if the game is determined under deterministic strategies.

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Marcin Przybyłko. 2014-08-26. Tree games with regular objectives. https://doi.org/10.4204/eptcs.161.20

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