Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Existential Theory of Equations with Rational Constraints in Free
  Groups is PSPACE-Complete   It is known that the existential theory of equations in free groups is
decidable. This is a famous result of Makanin. On the other hand it has been
shown that the scheme of his algorithm is not primitive recursive. In this
paper we present an algorithm that works in polynomial space, even in the more
general setting where each variable has a rational constraint, that is, the
solution has to respect a specification given by a regular word language. Our
main result states that the existential theory of equations in free groups with
rational constraints is PSPACE-complete. We obtain this result as a corollary
of the corresponding statement about free monoids with involution.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas