Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Backdoors to Nested Satisfiability   Knuth (1990) introduced the class of nested formulas and showed that their
satisfiability can be decided in polynomial time. We show that, parameterized
by the size of a smallest strong backdoor set to the target class of nested
formulas, checking the satisfiability of any CNF formula is fixed-parameter
tractable. Thus, for any k>0, the satisfiability problem can be solved in
polynomial time for any formula F for which there exists a variable set B of
size at most k such that for every truth assignment t to B, the formula F[t] is
nested; moreover, the degree of the polynomial is independent of k.
  Our algorithm uses the grid-minor theorem of Robertson and Seymour (1986) to
either find that the incidence graph of the formula has bounded treewidth - a
case that is solved using model checking for monadic second order logic - or to
find many vertex-disjoint obstructions in the incidence graph. For the latter
case, new combinatorial arguments are used to find a small backdoor set.
Combining both cases leads to an approximation algorithm producing a strong
backdoor set whose size is upper bounded by a function of the optimum. Going
through all assignments to this set of variables and using Knuth's algorithm,
the satisfiability of the input formula is decided.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph