Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free
  Graphs   We show that the class of chordal claw-free graphs admits LREC$_=$-definable
canonization. LREC$_=$ is a logic that extends first-order logic with counting
by an operator that allows it to formalize a limited form of recursion. This
operator can be evaluated in logarithmic space. It follows that there exists a
logarithmic-space canonization algorithm, and therefore a logarithmic-space
isomorphism test, for the class of chordal claw-free graphs. As a further
consequence, LREC$_=$ captures logarithmic space on this graph class. Since
LREC$_=$ is contained in fixed-point logic with counting, we also obtain that
fixed-point logic with counting captures polynomial time on the class of
chordal claw-free graphs.

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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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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: 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: math
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The categories of this paper are: patt-sol
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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: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg