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Probabilistic satisfiability: algorithms with the presence and absence of a phase transition

Probabilistic satisfiability: algorithms with the presence and absence of a phase transition We study algorithms for probabilistic satisfiability (PSAT), an NP-complete problem that is central to logic-probabilisti reasoning, focusing on the presence and absence of a phase transition phenomenon for each algorithm. Our study starts by defining a PSAT normal form, on which all algorithms are based. The proposed algorithms consist of several forms of reductions of PSAT to classical propositional satisfiability (SAT). The first algorithm is a canonical reduction of PSAT instances to SAT instances; three other algorithms are reductions to linear optimization with distinct column generation procedures, namely on auxiliary calls to SAT, weighted MAXSAT or SMT solvers. Theoretical and practical limitations of each algorithm are discussed. Several implementations were developed and compared by means of experiments using randomly generated input problems. Some of the implementations are shown to present a phase transition behavior. We show that variations of these algorithms may lead to the partial occlusion of the phase transition phenomenon and discuss the reasons for this change ofc practical behavior. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Probabilistic satisfiability: algorithms with the presence and absence of a phase transition

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References (59)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer International Publishing Switzerland
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-015-9466-6
Publisher site
See Article on Publisher Site

Abstract

We study algorithms for probabilistic satisfiability (PSAT), an NP-complete problem that is central to logic-probabilisti reasoning, focusing on the presence and absence of a phase transition phenomenon for each algorithm. Our study starts by defining a PSAT normal form, on which all algorithms are based. The proposed algorithms consist of several forms of reductions of PSAT to classical propositional satisfiability (SAT). The first algorithm is a canonical reduction of PSAT instances to SAT instances; three other algorithms are reductions to linear optimization with distinct column generation procedures, namely on auxiliary calls to SAT, weighted MAXSAT or SMT solvers. Theoretical and practical limitations of each algorithm are discussed. Several implementations were developed and compared by means of experiments using randomly generated input problems. Some of the implementations are shown to present a phase transition behavior. We show that variations of these algorithms may lead to the partial occlusion of the phase transition phenomenon and discuss the reasons for this change ofc practical behavior.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Jun 25, 2015

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