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Backdoors to Normality for Disjunctive Logic Programs

Backdoors to Normality for Disjunctive Logic Programs Backdoors to Normality for Disjunctive Logic Programs JOHANNES K. FICHTE, Vienna University of Technology and University of Potsdam STEFAN SZEIDER, Vienna University of Technology The main reasoning problems for disjunctive logic programs are complete for the second level of the polynomial hierarchy and hence considered harder than the same problems for normal (i.e., disjunction-free) programs, which are on the first level. We propose a new exact method for solving the disjunctive problems which exploits the small distance of a disjunctive programs from being normal. The distance is measured in terms of the size of a smallest "backdoor to normality," which is the smallest number of atoms whose deletion makes the program normal. Our method consists of three phases. In the first phase, a smallest backdoor is computed. We show that this can be done using an efficient algorithm for computing a smallest vertex cover of a graph. In the second phase, the backdoor is used to transform the logic program into a quantified Boolean formula (QBF) where the number of universally quantified variables equals the size of the backdoor and where the total size of the quantified Boolean formula is quasilinear in the size of the given logic http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Backdoors to Normality for Disjunctive Logic Programs

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References (106)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2015 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2818646
Publisher site
See Article on Publisher Site

Abstract

Backdoors to Normality for Disjunctive Logic Programs JOHANNES K. FICHTE, Vienna University of Technology and University of Potsdam STEFAN SZEIDER, Vienna University of Technology The main reasoning problems for disjunctive logic programs are complete for the second level of the polynomial hierarchy and hence considered harder than the same problems for normal (i.e., disjunction-free) programs, which are on the first level. We propose a new exact method for solving the disjunctive problems which exploits the small distance of a disjunctive programs from being normal. The distance is measured in terms of the size of a smallest "backdoor to normality," which is the smallest number of atoms whose deletion makes the program normal. Our method consists of three phases. In the first phase, a smallest backdoor is computed. We show that this can be done using an efficient algorithm for computing a smallest vertex cover of a graph. In the second phase, the backdoor is used to transform the logic program into a quantified Boolean formula (QBF) where the number of universally quantified variables equals the size of the backdoor and where the total size of the quantified Boolean formula is quasilinear in the size of the given logic

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Nov 14, 2015

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