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arXiv · 1710.05582

Modulo Counting on Words and Trees

Bartosz Bednarczyk·Witold Charatonik
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Abstract

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a technique for deciding the satisfiability problem. In the case of words this gives a new proof of EXPSPACE upper bound, and in the case of trees it gives a 2EXPTIME algorithm. This algorithm is optimal: we prove a matching lower bound by a generic reduction from alternating Turing machines working in exponential space; the reduction involves a development of a new version of tiling games.

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Bartosz Bednarczyk, Witold Charatonik. 2017-10-16. Modulo Counting on Words and Trees. https://arxiv.org/abs/1710.05582

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