Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Holant problems by winding   We give an FPRAS for Holant problems with parity constraints and
not-all-equal constraints, a generalisation of the problem of counting
sink-free-orientations. The approach combines a sampler for near-assignments of
"windable" functions -- using the cycle-unwinding canonical paths technique of
Jerrum and Sinclair -- with a bound on the weight of near-assignments. The
proof generalises to a larger class of Holant problems; we characterise this
class and show that it cannot be extended by expressibility reductions.
  We then ask whether windability is equivalent to expressibility by matchings
circuits (an analogue of matchgates), and give a positive answer for functions
of arity three.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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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: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th