New Encodings of Pseudo-Boolean Constraints into CNF

This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that realizes both of the desired properties. From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.

[1]  Joost P. Warners,et al.  A Linear-Time Transformation of Linear Inequalities into Conjunctive Normal Form , 1998, Inf. Process. Lett..

[2]  Philipp Hertel,et al.  Formalizing Dangerous SAT Encodings , 2007, SAT.

[3]  Igor L. Markov,et al.  Generic ILP versus specialized 0-1 ILP: an update , 2002, IEEE/ACM International Conference on Computer Aided Design, 2002. ICCAD 2002..

[4]  Olivier Bailleux,et al.  Efficient CNF Encoding of Boolean Cardinality Constraints , 2003, CP.

[5]  Michael D. Ernst,et al.  Automatic SAT-Compilation of Planning Problems , 1997, IJCAI.

[6]  James M. Crawford,et al.  Experimental Results on the Application of Satisfiability Algorithms to Scheduling Problems , 1994, AAAI.

[7]  Fahiem Bacchus,et al.  GAC Via Unit Propagation , 2007, CP.

[8]  Francesca Rossi,et al.  Principles and Practice of Constraint Programming – CP 2003 , 2003, Lecture Notes in Computer Science.

[9]  Joao Marques-Silva,et al.  Theory and Applications of Satisfiability Testing - SAT 2007, 10th International Conference, Lisbon, Portugal, May 28-31, 2007, Proceedings , 2007, SAT.

[10]  Jussi Rintanen,et al.  Modeling and solving diagnosis of discrete-event systems via satisfiability , 2007 .

[11]  Peter van Beek,et al.  Principles and Practice of Constraint Programming - CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1-5, 2005, Proceedings , 2005, CP.

[12]  Carsten Sinz,et al.  Towards an Optimal CNF Encoding of Boolean Cardinality Constraints , 2005, CP.

[13]  Ian P. Gent.  Arc Consistency in SAT , 2002, ECAI.

[14]  Niklas Sörensson,et al.  Translating Pseudo-Boolean Constraints into SAT , 2006, J. Satisf. Boolean Model. Comput..

[15]  Karem A. Sakallah,et al.  Pueblo: a modern pseudo-Boolean SAT solver , 2005, Design, Automation and Test in Europe.

[16]  Parosh Aziz Abdulla,et al.  Symbolic Reachability Analysis Based on SAT-Solvers , 2000, TACAS.

[17]  Masahiro Fujita,et al.  Symbolic model checking using SAT procedures instead of BDDs , 1999, DAC '99.

[18]  Olivier Roussel,et al.  A Translation of Pseudo Boolean Constraints to SAT , 2006, J. Satisf. Boolean Model. Comput..

[19]  Peter J. Stuckey,et al.  Flexible, Rule-Based Constraint Model Linearisation , 2008, PADL.

[20]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.