Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifier Alternation in Two-Variable First-Order Logic with Successor
  Is Decidable   We consider the quantifier alternation hierarchy within two-variable
first-order logic FO^2[<,suc] over finite words with linear order and binary
successor predicate. We give a single identity of omega-terms for each level of
this hierarchy. This shows that it is decidable for a given regular language
and a non-negative integer m, whether the language is definable by a formula in
FO^2[<,suc] which has at most m quantifier alternations. We also consider the
alternation hierarchy of unary temporal logic TL[X,F,Y,P] defined by the
maximal number of nested negations. This hierarchy coincides with the
FO^2[<,suc] alternation hierarchy.

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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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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: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ