Bridging Constraint Satisfaction and Boolean Satisfiability

This book provides a significant step towards bridging the areas of Boolean satisfiability and constraint satisfaction by answering the question why SAT-solvers are efficient on certain classes of CSP instances which are hard to solve for standard constraint solvers. The author also gives theoretical reasons for choosing a particular SAT encoding for several important classes of CSP instances. Boolean satisfiability and constraint satisfaction emerged independently as new fields of computer science, and different solving techniques have become standard for problem solving in the two areas. Even though any propositional formula (SAT) can be viewed as an instance of the general constraint satisfaction problem (CSP), the implications of this connection have only been studied in the last few years. The book will be useful for researchers and graduate students in artificial intelligence and theoretical computer science.

[1]  Phokion G. Kolaitis,et al.  Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics , 2002, CP.

[2]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[3]  Eugene C. Freuder.  A Sufficient Condition for Backtrack-Free Search , 1982, JACM.

[4]  Christophe Lecoutre,et al.  Backjump-based techniques versus conflict-directed heuristics , 2004, 16th IEEE International Conference on Tools with Artificial Intelligence.

[5]  Balakrishnan Krishnamurthy.  Short proofs for tricky formulas , 2004, Acta Informatica.

[6]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[7]  Eugene C. Freuder.  A sufficient condition for backtrack-bounded search , 1985, JACM.

[8]  Rina Dechter,et al.  Tractable Structures for Constraint Satisfaction Problems , 2006, Handbook of Constraint Programming.

[9]  Jun Gu,et al.  Algorithms for the satisfiability (SAT) problem: A survey , 1996, Satisfiability Problem: Theory and Applications.

[10]  Pascal Van Hentenryck,et al.  Constraint Satisfaction over Connected Row Convex Constraints , 1997, Artif. Intell..

[11]  Armin Biere,et al.  Extended Resolution Proofs for Conjoining BDDs , 2006, CSR.

[12]  Marc Gyssens,et al.  Closure properties of constraints , 1997, JACM.

[13]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[14]  Cesare Tinelli,et al.  Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T) , 2006, JACM.

[15]  Philippe Jégou,et al.  Hybrid backtracking bounded by tree-decomposition of constraint networks , 2003, Artif. Intell..

[16]  Rina Dechter,et al.  Backjump-based backtracking for constraint satisfaction problems , 2002, Artif. Intell..

[17]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002 .

[18]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[19]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

[20]  Christian Bessiere,et al.  Some Practicable Filtering Techniques for the Constraint Satisfaction Problem , 1997, IJCAI.

[21]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

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

[23]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[24]  Toby Walsh,et al.  Encodings of Non-Binary Constraint Satisfaction Problems , 1999, AAAI/IAAI.

[25]  Ashish Sabharwal,et al.  SymChaff: A Structure-Aware Satisfiability Solver , 2005, AAAI.

[26]  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).

[27]  Rina Dechter,et al.  Resolution versus Search: Two Strategies for SAT , 2000, Journal of Automated Reasoning.

[28]  Eugene C. Freuder.  Complexity of K-Tree Structured Constraint Satisfaction Problems , 1990, AAAI.

[29]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[30]  Thomas Schiex,et al.  Max-CSP competition 2008: toulbar2 solver description , 2008 .

[31]  Eugene C. Freuder,et al.  Constraint Satisfaction: An Emerging Paradigm , 2006, Handbook of Constraint Programming.

[32]  Martin Grohe,et al.  The Structure of Tractable Constraint Satisfaction Problems , 2006, MFCS.

[33]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

[34]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[35]  Mark E. Stickel,et al.  Implementing the Davis–Putnam Method , 2000, Journal of Automated Reasoning.

[36]  Joao Marques-Silva,et al.  The Impact of Branching Heuristics in Propositional Satisfiability Algorithms , 1999, EPIA.

[37]  Lakhdar Sais,et al.  Recording and Minimizing Nogoods from Restarts , 2007, J. Satisf. Boolean Model. Comput..

[38]  Ian P. Gent,et al.  Common Subexpression Elimination in Automated Constraint Modelling , 2008 .

[39]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[40]  Barry O'Sullivan,et al.  Value Ordering for Finding All Solutions: Interactions with Adaptive Variable Ordering , 2011, CP.

[41]  Mutsunori Banbara,et al.  Compiling Finite Linear CSP into SAT , 2006, CP.

[42]  Thomas C. Henderson,et al.  Arc and Path Consistency Revisited , 1986, Artif. Intell..

[43]  Warwick Harvey,et al.  Essence: A constraint language for specifying combinatorial problems , 2007, Constraints.

[44]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[45]  Peter Jeavons,et al.  A Survey of Tractable Constraint Satisfaction Problems , 1997 .

[46]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[47]  Toby Walsh,et al.  SAT v CSP , 2000, CP.

[48]  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).

[49]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[50]  Christian Bessiere,et al.  Optimal and Suboptimal Singleton Arc Consistency Algorithms , 2005, IJCAI.

[51]  John Martin,et al.  A History of Satisfiability , 2009, Handbook of Satisfiability.

[52]  Peter J. Stuckey,et al.  MiniZinc: Towards a Standard CP Modelling Language , 2007, CP.

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

[54]  Inês Lynce,et al.  The Puzzling Role of Simplification in Propositional Satisfiability , 2001 .

[55]  Ian P. Gent,et al.  Data Structures for Generalised Arc Consistency for Extensional Constraints , 2007, AAAI.

[56]  Ian P. Gent,et al.  Minion: A Fast Scalable Constraint Solver , 2006, ECAI.

[57]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[58]  Phokion G. Kolaitis,et al.  A Game-Theoretic Approach to Constraint Satisfaction , 2000, AAAI/IAAI.

[59]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[60]  Chia-Hoang Lee,et al.  Comments on Mohr and Henderson's Path Consistency Algorithm , 1988, Artif. Intell..

[61]  John N. Hooker,et al.  Integrated methods for optimization , 2011, International series in operations research and management science.

[62]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

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

[64]  Marc Gyssens,et al.  Decomposing Constraint Satisfaction Problems Using Database Techniques , 1994, Artif. Intell..

[65]  Georg Gottlob,et al.  A Comparison of Structural CSP Decomposition Methods , 1999, IJCAI.

[66]  Rina Dechter,et al.  Network-based heuristics for constraint satisfaction problems , 1988 .

[67]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.

[68]  Christopher Jefferson,et al.  Structural Tractability of Propagated Constraints , 2008, CP.

[69]  Peter J. Stuckey,et al.  Lazy Clause Generation Reengineered , 2009, CP.

[70]  Martin Grohe,et al.  The complexity of homomorphism and constraint satisfaction problems seen from the other side , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[71]  Stanislav Zivny,et al.  Classes of submodular constraints expressible by graph cuts , 2008, Constraints.

[72]  Johan de Kleer,et al.  A Comparison of ATMS and CSP Techniques , 1989, IJCAI.

[73]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[74]  Peter van Beek,et al.  An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint , 2005, Constraints.

[75]  Jinbo Huang.  Universal Booleanization of Constraint Models , 2008, CP.

[76]  Manuel Bodirsky,et al.  Equivalence Constraint Satisfaction Problems , 2012, CSL.

[77]  Holger H. Hoos.  SAT-Encodings, Search Space Structure, and Local Search Performance , 1999, IJCAI.

[78]  Rina Dechter,et al.  Look-Ahead Value Ordering for Constraint Satisfaction Problems , 1995, IJCAI.

[79]  Patrick Prosser,et al.  HYBRID ALGORITHMS FOR THE CONSTRAINT SATISFACTION PROBLEM , 1993, Comput. Intell..

[80]  Holger H. Hoos,et al.  Local Search Methods , 2006, Handbook of Constraint Programming.

[81]  Adnan Darwiche,et al.  On the Power of Clause-Learning SAT Solvers with Restarts , 2009, CP.

[82]  Phokion G. Kolaitis,et al.  Conjunctive-Query Containment and Constraint Satisfaction , 2000, J. Comput. Syst. Sci..

[83]  Sharad Malik,et al.  The Quest for Efficient Boolean Satisfiability Solvers , 2002, CAV.

[84]  Eugene C. Freuder,et al.  Contradicting Conventional Wisdom in Constraint Satisfaction , 1994, ECAI.

[85]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[86]  Eugene C. Freuder,et al.  Partial Constraint Satisfaction , 1989, IJCAI.

[87]  David G. Mitchell,et al.  2-Way vs. d-Way Branching for CSP , 2005, CP.

[88]  Joao Marques-Silva,et al.  GRASP-A new search algorithm for satisfiability , 1996, Proceedings of International Conference on Computer Aided Design.

[89]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[90]  Pascal Van Hentenryck,et al.  A Generic Arc-Consistency Algorithm and its Specializations , 1992, Artif. Intell..