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The Complexity of Read-Once Resolution

The Complexity of Read-Once Resolution We investigate the complexity of deciding whether a propositional formula has a read-once resolution proof. We give a new and general proof of Iwama–Miynano's theorem which states that the problem whether a formula has a read-once resolution proof is NP-complete. Moreover, we show for fixed k≥2 that the additional restriction that in each resolution step one of the parent clauses is a k-clause preserves the NP-completeness. If we demand that the formulas are minimal unsatisfiable and read-once refutable then the problem remains NP-complete. For the subclasses MU(k) of minimal unsatisfiable formulas we present a pol-time algorithm deciding whether a MU(k)-formula has a read-once resolution proof. Furthermore, we show that the problems whether a formula contains a MU(k)-subformula or a read-once refutable MU(k)-subformula are NP-complete. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

The Complexity of Read-Once Resolution

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1023/A:1016339119669
Publisher site
See Article on Publisher Site

Abstract

We investigate the complexity of deciding whether a propositional formula has a read-once resolution proof. We give a new and general proof of Iwama–Miynano's theorem which states that the problem whether a formula has a read-once resolution proof is NP-complete. Moreover, we show for fixed k≥2 that the additional restriction that in each resolution step one of the parent clauses is a k-clause preserves the NP-completeness. If we demand that the formulas are minimal unsatisfiable and read-once refutable then the problem remains NP-complete. For the subclasses MU(k) of minimal unsatisfiable formulas we present a pol-time algorithm deciding whether a MU(k)-formula has a read-once resolution proof. Furthermore, we show that the problems whether a formula contains a MU(k)-subformula or a read-once refutable MU(k)-subformula are NP-complete.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Oct 10, 2004

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