Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of finite-variable fragments of propositional modal logics of
  symmetric frames   While finite-variable fragments of the propositional modal logic S5--complete
with respect to reflexive, symmetric and transitive frames--are polynomial-time
decidable, the restriction to finite-variable formulas for logics of reflexive
and transitive frames yields fragments that remain "intractable." The role of
the symmetry condition in this context has not been investigated. We show that
symmetry either by itself or in combination with reflexivity produces logics
that behave just like logics of reflexive and transitive frames, i.e. their
finite-variable fragments remain intractable, namely PSPACE-hard. This raises
the question of where exactly the borderline lies between modal logics whose
finite-variable fragments are tractable and the rest.

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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int