DMCA
Elliptic Approximations of Propositional Formulae (1996)
| Venue: | Discrete Appl. Math |
| Citations: | 9 - 4 self |
BibTeX
@ARTICLE{Maaren96ellipticapproximations,
author = {Hans Van Maaren},
title = {Elliptic Approximations of Propositional Formulae},
journal = {Discrete Appl. Math},
year = {1996},
volume = {96},
pages = {96--97}
}
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Abstract
. A propositional formula can be approximated by a concave quadratic function. This approximation is obtained as a second order Taylor expansion of a convex smooth model. It is shown that in the 3- SAT case, the involved parameters can be set to such values that yield optimal discriminative properties. Two concentric (generally elliptic) quadratic convex regions are established, the inner one containing only satisfiable assignments and the outer one excluding the average non satisfiable assignment and including all satisfiable assignments. Keywords. Satisfiability, convexity, quadratic approximations, quadratic valid cuts. 1991 Mathematics Subject Classification. Primary 68Q25,90C09, Secondary 90C10, 90C27. 1 Introduction. Smooth convex and concave transforms of propositional formulae were introduced by van Maaren, Groote and Rozema in [4]. In [5] the eigenvalues of the associated Hessian matrices were used to design a branching variable heuristic which has (experimentally) been sh...
Keyphrases
propositional formula elliptic approximation satisfiable assignment associated hessian matrix mathematics subject classification convex smooth model smooth convex average non satisfiable assignment concave quadratic function quadratic approximation optimal discriminative property involved parameter quadratic valid cut sat case van maaren quadratic convex region second order taylor expansion branching variable heuristic
