The First-Order Theory of Ground Tree Rewrite Graphs

Details The First-Order Theory of Ground Tree Rewrite Graphs The First-Order Theory of Ground Tree Rewrite Graphs

2011-07-05

arxiv.org/abs/1107.0919v2

Computer Science

Logic in Computer Science

Scientific paper

We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

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