Extensions and Variants of Dalal's Quad Polynomial Fragments of SAT

An extension and several variants of Dalal's Quad polynomial fragments of SAT are presented. Firstly, the stability of Quad fragments is investigated. Then, the extension is as follows. Quad fixed total orderings of clauses is accompanied with specific additional separate orderings of maximal sub-clauses. Interestingly, the resulting fragments extend Quad without degrading its worst-case complexity. Several other variants of Quad that give rise to additional different polynomial fragments are then investigated.

[1]  Lakhdar Sais,et al.  Automatic Extraction of Functional Dependencies , 2004, SAT.

[2]  Lakhdar Sais,et al.  Eliminating redundancies in SAT search trees , 2003, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence.

[3]  Daniel Le Berre.  Exploiting the real power of unit propagation lookahead , 2001, Electron. Notes Discret. Math..

[4]  Lakhdar Sais,et al.  Reducing hard SAT instances to polynomial ones , 2007, 2007 IEEE International Conference on Information Reuse and Integration.

[5]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[6]  Lakhdar Sais,et al.  About some UP-based polynomial fragments of SAT , 2015, Annals of Mathematics and Artificial Intelligence.

[7]  Eli Ben-Sasson,et al.  Short proofs are narrow—resolution made simple , 2001, JACM.

[8]  John N. Hooker,et al.  Extended Horn sets in propositional logic , 1991, JACM.

[9]  Allen Van Gelder,et al.  A perspective on certain polynomial-time solvable classes of satisfiability , 2003, Discret. Appl. Math..

[10]  Harry R. Lewis,et al.  Renaming a Set of Clauses as a Horn Set , 1978, JACM.

[11]  Gérard Cornuéjols,et al.  Balanced matrices , 2006, Discret. Math..

[12]  Lakhdar Sais,et al.  Using Boolean Constraint Propagation for Sub-clauses Deduction , 2005, CP.

[13]  Zvi Galil.  On Resolution with Clauses of Bounded Size , 1977, SIAM J. Comput..

[14]  Ondrej Cepek,et al.  Properties of SLUR Formulae , 2012, SOFSEM.

[15]  Chu Min Li,et al.  Look-Ahead Versus Look-Back for Satisfiability Problems , 1997, CP.

[16]  Mukesh Dalal,et al.  An Almost Quadratic Class of Satisfiability Problems , 1996, ECAI.

[17]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[18]  Zvi Galil,et al.  On the validity and complexity of bounded resolution , 1975, STOC.

[19]  Craig A. Tovey,et al.  A simplified NP-complete satisfiability problem , 1984, Discret. Appl. Math..

[20]  Toniann Pitassi,et al.  Simplified and improved resolution lower bounds , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[21]  Václav Vlcek,et al.  On hierarchies over the SLUR class , 2012, ISAIM.