Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the expressive power of permanents and perfect matchings of matrices
  of bounded pathwidth/cliquewidth   Some 25 years ago Valiant introduced an algebraic model of computation in
order to study the complexity of evaluating families of polynomials. The theory
was introduced along with the complexity classes VP and VNP which are analogues
of the classical classes P and NP. Families of polynomials that are difficult
to evaluate (that is, VNP-complete) includes the permanent and hamiltonian
polynomials. In a previous paper the authors together with P. Koiran studied
the expressive power of permanent and hamiltonian polynomials of matrices of
bounded treewidth, as well as the expressive power of perfect matchings of
planar graphs. It was established that the permanent and hamiltonian
polynomials of matrices of bounded treewidth are equivalent to arithmetic
formulas. Also, the sum of weights of perfect matchings of planar graphs was
shown to be equivalent to (weakly) skew circuits. In this paper we continue the
research in the direction described above, and study the expressive power of
permanents, hamiltonians and perfect matchings of matrices that have bounded
pathwidth or bounded cliquewidth. In particular, we prove that permanents,
hamiltonians and perfect matchings of matrices that have bounded pathwidth
express exactly arithmetic formulas. This is an improvement of our previous
result for matrices of bounded treewidth. Also, for matrices of bounded
weighted cliquewidth we show membership in VP for these polynomials.

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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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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: stat
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The categories of this paper are: alg-geom