
Subexponential complexity of regular linear CNF formulas
The study of regular linear conjunctive normal form (LCNF) formulas is o...
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VCdimension of short Presburger formulas
We study VCdimension of short formulas in Presburger Arithmetic, define...
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Towards Understanding and Harnessing the Potential of Clause Learning
Efficient implementations of DPLL with the addition of clause learning a...
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VC density of set systems defnable in treelike graphs
We study set systems definable in graphs using variants of logic with di...
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Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity
We significantly strengthen and generalize the theorem lifting Nullstell...
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An Optimal Construction for the BarthelmannSchwentick Normal Form on Classes of Structures of Bounded Degree
Building on the locality conditions for firstorder logic by Hanf and Ga...
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Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs
We show exponential lower bounds on resolution proof length for pigeonho...
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Characterizing Tseitinformulas with short regular resolution refutations
Tseitinformulas 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 Tseitinformulas 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(logV(G)). To do so, we show that any regular resolution refutation of an unsatisfiable Tseitinformula with graph G of bounded degree has length 2^Ω(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 Tseitinformulas to the size of representations of satisfiable Tseitinformulas in decomposable negation normal form (DNNF). Then we prove that for every graph G of bounded degree, every DNNFrepresentation of every satisfiable Tseitinformula with graph G must have size 2^Ω(tw(G)) which yields our lower bound for regular resolution.
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