Abstract
We contribute to the question about decidability of first-order logic on configuration graphs of collapsible pushdown automata. Our first result is decidability of existential FO sentences on configuration graphs (and their ε-closures) of collapsible pushdown automata of order 3, restricted to reachable configurations. Our second result is undecidability of the whole first-order logic on configuration graphs which are not restricted to reachable configurations, but are restricted to constructible stacks. Our third result is decidability of first-order logic on configuration graphs (for arbitrary order of automata) which are not restricted to reachable configurations nor to constructible stacks, under an alternative definition of stacks, called annotated stacks.
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Parys, P. (2014). First-Order Logic on CPDA Graphs. In: Hirsch, E.A., Kuznetsov, S.O., Pin, JÉ., Vereshchagin, N.K. (eds) Computer Science - Theory and Applications. CSR 2014. Lecture Notes in Computer Science, vol 8476. Springer, Cham. https://doi.org/10.1007/978-3-319-06686-8_23
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DOI: https://doi.org/10.1007/978-3-319-06686-8_23
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