Abstract
Two-way alternating automata on infinite trees were introduced by Vardi (Reasoning about the part with two way automata, Lecture Notes in Computer Science, vol. 11, Springer, Berlin, 1998, pp. 628–641). Here we consider alternating two-way automata on graphs and show the decidability of the following problem: “does a given automaton with the Büchi condition accept any finite graph?” Using this result we demonstrate the decidability of the finite model problem for a certain fragment of the modal μ-calculus with backward modalities.
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