Model Checking Games for the Alternation-Free µ-Calculus and Alternating Automata

• Authors: Martin Leucker
• Venue: LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
• Year: 1999

We relate game-based model checking and model checking via 1-letter simple weak alternating Büchi automata (ISWABA) 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. ISWABA sire a restricted class of alternating Büchi automata and were defined in [BVW94]. They admit efficient automata-based model checking for CTL amd the alternation-free µcalculus. We give an interpretation for these automata in terms of gcime 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 ISWABA 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 getmes.