Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Time Complexity of the Permanent and the Tutte Polynomial   We show conditional lower bounds for well-studied #P-hard problems:
  (a) The number of satisfying assignments of a 2-CNF formula with n variables
cannot be counted in time exp(o(n)), and the same is true for computing the
number of all independent sets in an n-vertex graph.
  (b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed
in time exp(o(n)).
  (c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time
exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it
cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs.
  Our lower bounds are relative to (variants of) the Exponential Time
Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF
formulas cannot be decided in time exp(o(n)). We relax this hypothesis by
introducing its counting version #ETH, namely that the satisfying assignments
cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds,
we transfer the sparsification lemma for d-CNF formulas to the counting
setting.

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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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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: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph