# Solving SAT for CNF formulas with a one-sided restriction on variable occurrences

Johannsen, D. and Razgon, Igor and Wahlström, M.
(2009)
Solving SAT for CNF formulas with a one-sided restriction on variable occurrences.
In:
Kullmann, O. (ed.)
*Theory and Applications of Satisfiability Testing.*
Lecture Notes in Computer Science 5584.
Berlin, Germany:
Springer Verlag, pp. 80-85.
ISBN 9783642027765.

## Abstract

In this paper we consider the class of boolean formulas in Conjunctive Normal Form (CNF) where for each variable all but at most d occurrences are either positive or negative. This class is a generalization of the class of CNF formulas with at most d occurrences (positive and negative) of each variable which was studied in [Wahlström, 2005]. Applying complement search [Purdom, 1984], we show that for every d there exists a constant γd<2−12d+1 such that satisfiability of a CNF formula on n variables can be checked in runtime \ensuremathO(γnd) if all but at most d occurrences of each variable are either positive or negative. We thoroughly analyze the proposed branching strategy and determine the asymptotic growth constant γ d more precisely. Finally, we show that the trivial \ensuremathO(2n) barrier of satisfiability checking can be broken even for a more general class of formulas, namely formulas where the positive or negative literals of every variable have what we will call a d–covering. To the best of our knowledge, for the considered classes of formulas there are no previous non-trivial upper bounds on the complexity of satisfiability checking.

## Metadata

Item Type: | Book Section |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 01 Aug 2013 15:51 |

Last Modified: | 09 Aug 2023 12:34 |

URI: | https://eprints.bbk.ac.uk/id/eprint/7926 |

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