Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing Tseitin-formulas with short regular resolution
  refutations   Tseitin-formulas are systems of parity constraints whose structure is
described by a graph. These formulas have been studied extensively in proof
complexity as hard instances in many proof systems. In this paper, we prove
that a class of unsatisfiable Tseitin-formulas of bounded degree has regular
resolution refutations of polynomial length if and only if the treewidth of all
underlying graphs $G$ for that class is in $O(\log|V(G)|)$. To do so, we show
that any regular resolution refutation of an unsatisfiable Tseitin-formula with
graph $G$ of bounded degree has length $2^{\Omega(tw(G))}/|V(G)|$, thus
essentially matching the known $2^{O(tw(G))}poly(|V(G)|)$ upper bound up. Our
proof first connects the length of regular resolution refutations of
unsatisfiable Tseitin-formulas to the size of representations of
\textit{satisfiable} Tseitin-formulas in decomposable negation normal form
(DNNF). Then we prove that for every graph $G$ of bounded degree, every
DNNF-representation of every satisfiable Tseitin-formula with graph $G$ must
have size $2^{\Omega(tw(G))}$ which yields our lower bound for regular
resolution.

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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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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: chem-ph
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The categories of this paper are: comp-gas