Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal Theories for Logspace Counting   We introduce two-sorted theories in the style of Cook and Nguyen for the
complexity classes ParityL and DET, whose complete problems include
determinants over GF(2) and Z, respectively. The definable functions in these
theories are the functions in the corresponding complexity classes; thus each
theory formalizes reasoning using concepts from its corresponding complexity
class.

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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: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: nlin