Parallel Resolution of the Satisfiability Problem: A Survey

The past few years have seen enormous progress in the performance of propositional satisfiability (SAT) solvers, and consequently SAT solvers are widely used in industry for many applications. In spite of this progress, there is strong demand for higher SAT algorithms efficiency to solve harder and larger problems. Unfortunately, most modern solvers are sequential and fewer are parallel. Our intention is to review the work of this last decade on parallel resolution of SAT with DPLL solvers which are the most widely used complete ones.

[1]  Sharad Malik,et al.  Cache Performance of SAT Solvers: a Case Study for Efficient Implementation of Algorithms , 2003, SAT.

[2]  Nachum Dershowitz,et al.  Parallel Multithreaded Satisfiability Solver: Design and Implementation , 2005, PDMC.

[3]  Chu Min Li,et al.  Integrating Equivalency Reasoning into Davis-Putnam Procedure , 2000, AAAI/IAAI.

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

[5]  Hantao Zhang,et al.  SATO: An Efficient Propositional Prover , 1997, CADE.

[6]  Hans van Maaren,et al.  A two phase algorithm for solving a class of hard satissfiability problems , 1998 .

[7]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[8]  Daniel Sheridan,et al.  The Optimality of a Fast CNF Conversion and its Use with SAT , 2004, SAT.

[9]  Adnan Darwiche.  Compiling Knowledge into Decomposable Negation Normal Form , 1999, IJCAI.

[10]  Panos M. Pardalos,et al.  A Parallel GRASP for MAX-SAT Problems , 1996, PARA.

[11]  Hachemi Bennaceur.  The Satisfiability Problem Regarded as a Constraint Satisfaction Problem , 1996, ECAI.

[12]  Gilles Dequen,et al.  A backbone-search heuristic for efficient solving of hard 3-SAT formulae , 2001, IJCAI.

[13]  Gil Utard,et al.  Parallelizing Satz Using Dynamic Workload Balancing , 2001, Electron. Notes Discret. Math..

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

[15]  Thomas Stützle,et al.  A review of the literature on local search algorithms for MAX-SAT , 2001 .

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

[17]  Maria Paola Bonacina,et al.  PSATO: a Distributed Propositional Prover and its Application to Quasigroup Problems , 1996, J. Symb. Comput..

[18]  Hans van Maaren,et al.  Sat2000: Highlights of Satisfiability Research in the Year 2000 , 2000 .

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

[20]  Oliver Vornberger,et al.  Superlinear Speedup for Parallel Backtracking , 1987, ICS.

[21]  Udi Manber,et al.  DIB—a distributed implementation of backtracking , 1987, TOPL.

[22]  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).

[23]  Ian P. Gent,et al.  Parallel heuristic search in Haskell , 2000, Scottish Functional Programming Workshop.

[24]  Laurent Simon,et al.  Fifty-Five Solvers in Vancouver: The SAT 2004 Competition , 2004, SAT (Selected Papers.

[25]  Andrea Roll.  Criticality and Parallelism in GSAT , 2001, Electron. Notes Discret. Math..

[26]  M. Bonacina,et al.  Cumulating search in a distributed computing environment: a case study in parallel satisfiability , 1994 .

[27]  Yasuo Okabe,et al.  Parallelizing local search for CNF satisfiability using vectorization and PVM , 2000, JEAL.

[28]  Wen-Tsuen Chen,et al.  A parallel approach for theorem proving in prepositional logic , 1987, Inf. Sci..

[29]  Per Bjesse,et al.  Guiding SAT Diagnosis with Tree Decompositions , 2003, SAT.

[30]  Jon M. Kleinberg,et al.  A deterministic (2-2/(k+1))n algorithm for k-SAT based on local search , 2002, Theor. Comput. Sci..

[31]  C. Y. Tang,et al.  Solving the Satisfiability Problem by Using Randomized Approach , 1992, Inf. Process. Lett..

[32]  Vipin Kumar,et al.  On the Efficiency of Parallel Backtracking , 1993, IEEE Trans. Parallel Distributed Syst..

[33]  Fumiaki Okushi.  Parallel cooperative propositional theorem proving , 2004, Annals of Mathematics and Artificial Intelligence.

[34]  Iouliia Skliarova,et al.  Reconfigurable Hardware SAT Solvers: A Survey of Systems , 2003, FPL.

[35]  Ewald Speckenmeyer,et al.  Solving satisfiability in less than 2n steps , 1985, Discret. Appl. Math..

[36]  Karem A. Sakallah,et al.  GRASP—a new search algorithm for satisfiability , 1996, ICCAD 1996.

[37]  Yanjun Zhang,et al.  Efficiency of Randomized Parallel Backtrack Search , 1999, Algorithmica.

[38]  Richard M. Karp,et al.  Randomized parallel algorithms for backtrack search and branch-and-bound computation , 1993, JACM.

[39]  Michaël Krajecki,et al.  Decomposition techniques for parallel resolution of constraint satisfaction problems in shared memory: a comparative study , 2005, Int. J. Comput. Sci. Eng..

[40]  R. Wolski,et al.  GridSAT: A Chaff-based Distributed SAT Solver for the Grid , 2003, ACM/IEEE SC 2003 Conference (SC'03).

[41]  Fabio Massacci,et al.  Logical Cryptanalysis as a SAT Problem , 2000, Journal of Automated Reasoning.

[42]  Gilles Dequen,et al.  kcnfs: An Efficient Solver for Random k-SAT Formulae , 2003, SAT.

[43]  Jack Dongarra,et al.  MPI: The Complete Reference , 1996 .

[44]  Hans van Maaren,et al.  Aligning CNF- and Equivalence-reasoning , 2004, SAT.

[45]  Peter Baumgartner,et al.  The Taming of the (X)OR , 2000, Computational Logic.

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

[47]  Bernard Jurkowiak.  Programmation haute performance pour la résolution des problèmes SAT et CSP , 2004 .

[48]  Sheila A. McIlraith,et al.  Partition-based logical reasoning for first-order and propositional theories , 2005, Artif. Intell..

[49]  Toby Walsh,et al.  Solving Non-clausal Formulas with DPLL search , 2004, SAT.

[50]  Tad Hogg,et al.  Expected Gains from Parallelizing Constraint Solving for Hard Problems , 1994, AAAI.

[51]  Oliver Kullmann,et al.  Investigations on autark assignments , 2000, Discret. Appl. Math..

[52]  Chu Min Li,et al.  On the limit of branching rules for hard random unsatisfiable 3-SAT , 2003, Discret. Appl. Math..

[53]  Wolfgang Küchlin,et al.  Parallel propositional satisfiability checking with distributed dynamic learning , 2003, Parallel Comput..

[54]  Wolfgang Küchlin,et al.  PaSAT - Parallel SAT-Checking with Lemma Exchange: Implementation and Applications , 2001, Electron. Notes Discret. Math..

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