Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One Quantifier Alternation in First-Order Logic with Modular Predicates   Adding modular predicates yields a generalization of first-order logic FO
over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and
predicates for $x \equiv i \mod n$ has been investigated by Barrington,
Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated
by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that
definability in the two-variable fragment FO2[<,MOD] is decidable. In this
paper we continue this line of work.
  We give an effective algebraic characterization of the word languages in
Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex
normal form with two blocks of quantifiers starting with an existential block.
In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD]
which is closed under negation, has the same expressive power as two-variable
logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and
Wilke to modular predicates. As a byproduct, we obtain another decidable
characterization of FO2[<,MOD].

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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn