
XSAT of Exact Linear CNF Classes
It is shown that lregularity implies kuniformity in exact linear CNF f...
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Subexponential complexity of regular linear CNF formulas
The study of regular linear conjunctive normal form (LCNF) formulas is o...
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Positive Neural Networks in Discrete Time Implement MonotoneRegular Behaviors
We study the expressive power of positive neural networks. The model use...
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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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The Complexity of Aggregates over Extractions by Regular Expressions
Regular expressions with capture variables, also known as "regex formula...
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Enumerating models of DNF faster: breaking the dependency on the formula size
In this article, we study the problem of enumerating the models of DNF f...
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A compact formula for the derivative of a 3D rotation in exponential coordinates
We present a compact formula for the derivative of a 3D rotation matrix...
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XSAT of Linear CNF Formulas
Open questions with respect to the computational complexity of linear CNF formulas in connection with regularity and uniformity are addressed. In particular it is proven that any lregular monotone CNF formula is XSATunsatisfiable if its number of clauses m is not a multiple of l. For exact linear formulas one finds surprisingly that lregularity implies kuniformity, with m = 1 + k(l1)) and allowed kvalues obey k(k1) = 0 (mod l). Then the computational complexity of the class of monotone exact linear and lregular CNF formulas with respect to XSAT can be determined: XSATsatisfiability is either trivial, if m is not a multiple of l, or it can be decided in subexponential time, namely O(exp(n^^1/2)). Subexponential time behaviour for the wider class of regular and uniform linear CNF formulas can be shown for certain subclasses.
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