Automata for Nogood Recording in Constraint Satisfaction Problems

Nogood recording is a well known technique for reducing the thrash- ing encountered by tree search algorithms. One of the most significant disadvan- tages of nogood recording has been its prohibitive space complexity. In this paper we attempt to mitigate this by using an automaton to compactly represent a set of nogoods. We demonstrate how nogoods can be propagated using a known al- gorithm for achieving generalised arc consistency. Our experimental results on a number of benchmark problems demonstrate the utility of our approach.

[1]  Bruce W. Watson,et al.  Incremental construction of minimal acyclic finite state automata , 2000, CL.

[2]  Rina Dechter,et al.  Enhancement Schemes for Constraint Processing: Backjumping, Learning, and Cutset Decomposition , 1990, Artif. Intell..

[3]  Patrick Prosser,et al.  MAC-CBJ: maintaining arc consistency with conflict-directed backjumping , 1995 .

[4]  Daniel P. Miranker,et al.  A Complexity Analysis of Space-Bounded Learning Algorithms for the Constraint Satisfaction Problem , 1996, AAAI/IAAI, Vol. 1.

[5]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[6]  E BryantRandal.  Graph-Based Algorithms for Boolean Function Manipulation , 1986 .

[7]  Thomas Schiex,et al.  Nogood Recording for static and dynamic constraint satisfaction problems , 1993, Proceedings of 1993 IEEE Conference on Tools with Al (TAI-93).

[8]  Fahiem Bacchus,et al.  Generalized NoGoods in CSPs , 2005, AAAI.

[9]  Joao Marques-Silva,et al.  The Effect of Nogood Recording in MAC-CBJ SAT Algorithms , 2002 .

[10]  Lucas Bordeaux,et al.  Propositional Satisfiability and Constraint Programming: A comparative survey , 2006, CSUR.

[11]  Patrice Boizumault,et al.  Dynamic Backtracking with Constraint Propagation Application to static and dynamic CSPs , 1997 .

[12]  Nageshwara Rao Vempaty.  Solving Constraint Satisfaction Problems Using Finite State Automata , 1992, AAAI.

[13]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Exceptionally Hard SAT Instances , 1996, CP.

[14]  Thomas Schiex,et al.  Nogood Recording for Static and Dynamic Constraint Satisfaction Problems , 1994, Int. J. Artif. Intell. Tools.

[15]  Patrice Boizumault,et al.  k-relevant Explanations for Constraint Programming , 2003, FLAIRS.

[16]  Lakhdar Sais,et al.  Boosting Systematic Search by Weighting Constraints , 2004, ECAI.

[17]  Fahiem Bacchus,et al.  Unrestricted Nogood Recording in CSP Search , 2003, CP.

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  Inês Lynce,et al.  The Effect of Nogood Recording in DPLL-CBJ SAT Algorithms , 2002, International Workshop on Constraint Solving and Constraint Logic Programming.

[20]  Peter van Beek,et al.  Conflict-Directed Backjumping Revisited , 2011, J. Artif. Intell. Res..

[21]  V. N. Rao,et al.  Solving constraint satisfaction problems using finite state automata , 1992, AAAI 1992.

[22]  Simon de Givry,et al.  Radio Link Frequency Assignment , 1999, Constraints.

[23]  Christian Bessiere,et al.  Arc Consistency for General Constraint Networks: Preliminary Results , 1997, IJCAI.

[24]  Gilles Pesant,et al.  A Regular Language Membership Constraint for Finite Sequences of Variables , 2004, CP.

[25]  Gérard Ferrand,et al.  Correctness of Constraint Retraction Algorithms , 2003, FLAIRS.