
XSAT of Linear CNF Formulas
Open questions with respect to the computational complexity of linear CN...
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Subexponential Upper Bound for #XSAT of some CNF Classes
We derive an upper bound on the number of models for exact satisfiabilit...
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Characterizing Tseitinformulas with short regular resolution refutations
Tseitinformulas are systems of parity constraints whose structure is de...
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The Expressiveness of Looping Terms in the Semantic Programming
We consider the complexity of reasoning in extensions of the language of...
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ScanSSD: Scanning Single Shot Detector for Mathematical Formulas in PDF Document Images
We introduce the Scanning Single Shot Detector (ScanSSD) for locating ma...
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Computing the Homology of Semialgebraic Sets. II: General formulas
We describe and analyze an algorithm for computing the homology (Betti n...
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Computing the Homology of Semialgebraic Sets I: Lax Formulas
We describe and analyze an algorithm for computing the homology (Betti n...
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Subexponential complexity of regular linear CNF formulas
The study of regular linear conjunctive normal form (LCNF) formulas is of interest because exact satisfiability (XSAT) is known to be NPcomplete for this class of formulas. In a recent paper it was shown that the subclass of regular exact LCNF formulas (XLCNF) is of subexponential complexity, i.e. XSAT can be determined in subexponential time. Here I show that this class is just a subset of a larger class of LCNF formulas which display this very kind of complexity. To this end I introduce the property of disjointedness of LCNF formulas, measured, for a single clause C, by the number of clauses which have no variable in common with C. If for a given LCNF formula F all clauses have the same disjointedness d we call F ddisjointed and denote the class of such formulas by dLCNF. XLCNF formulas correspond to the special cased=0. One main result of the paper is that the class of all monotone lregular LCNF formulas which are ddisjointed, with d smaller than some upper bound D, is of subexponential complexity. This result can be generalized to show that all monotone, lregular LCNF formulas F which have a bounded mean disjointedness, are of subexponential XSATcomplexity, as well.
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