First-Order Logic on CPDA Graphs
نویسنده
چکیده
We contribute to the question about decidability of firstorder 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 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.
منابع مشابه
The Limits of Decidability for First Order Logic on CPDA Graphs
Higher-order pushdown automata (n-PDA) are abstract machines equipped with a nested ‘stack of stacks of stacks’. Collapsible pushdown automata (n-CPDA) extend these devices by adding ‘links’ to the stack and are equi-expressive for tree generation with simply typed λY terms. Whilst the configuration graphs of HOPDA are well understood, relatively little is known about the CPDA graphs. The order...
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