Abstract
We relate game-based model checking and model checking via 1-letter simple weak alternating Büchi automata (1SWABA) for the alternation-free μ-calculus. Game-based algorithms have the advantage that in addition to checking whether a formula is valid or not they determine a winning strategy which can be employed for explaining to the user why the formula is valid or not. 1SWABA are a restricted class of alternating Büchi automata and were defined in [BVW94]. They admit efficient automata-based model checking for CTL and the alternation-free μ-calculus. We give an interpretation for these automata in terms of game theory and show that this interpretation coincides with the notion of model checking games for CTL and the μ-calculus. Then we explain that the efficient non-emptiness procedure for 1SWABA presented in [BVW94] can also be understood as a game-based model checking procedure. Furthermore, we show that this algorithm is not only useful for checking the validity of a formula but also for determining a winning strategy for the winner of the underlying model checking game. In this way we obtain a linear time algorithm for model checking games.
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Leucker, M. (1999). Model Checking Games for the Alternation-Free μ-Calculus and Alternating Automata. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_6
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DOI: https://doi.org/10.1007/3-540-48242-3_6
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