Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modulo Counting on Words and Trees   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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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom