Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet ...

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

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

[3]  Olaf Beyersdorff,et al.  Parameterized Complexity of DPLL Search Procedures , 2011, SAT.

[4]  Klas Markström,et al.  Locality and Hard SAT-Instances , 2006, J. Satisf. Boolean Model. Comput..

[5]  J. P. Marques,et al.  GRASP : A Search Algorithm for Propositional Satisfiability , 1999 .

[6]  Neil Thapen A Tradeoff Between Length and Width in Resolution , 2014, Theory Comput..

[7]  Jakob Nordström,et al.  Long Proofs of (Seemingly) Simple Formulas , 2014, SAT.

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

[9]  Henry A. Kautz,et al.  Towards Understanding and Harnessing the Potential of Clause Learning , 2004, J. Artif. Intell. Res..

[10]  Krzysztof Czarnecki,et al.  Learning Rate Based Branching Heuristic for SAT Solvers , 2016, SAT.

[11]  Adnan Darwiche,et al.  A Lightweight Component Caching Scheme for Satisfiability Solvers , 2007, SAT.

[12]  Eli Ben-Sasson,et al.  Understanding Space in Proof Complexity: Separations and Trade-offs via Substitutions , 2011, ICS.

[13]  Justyna Petke,et al.  Tractable Benchmarks For Constraint Programming , 2009 .

[14]  Ivor T. A. Spence,et al.  Zero-One Designs Produce Small Hard SAT Instances , 2010, SAT.

[15]  Stephen A. Cook,et al.  The Relative Efficiency of Propositional Proof Systems , 1979, Journal of Symbolic Logic.

[16]  Maria Luisa Bonet,et al.  Optimality of size-width tradeoffs for resolution , 2001, computational complexity.

[17]  Chris Beck,et al.  Some trade-off results for polynomial calculus: extended abstract , 2013, STOC '13.

[18]  Jinbo Huang,et al.  The Effect of Restarts on the Efficiency of Clause Learning , 2007, IJCAI.

[19]  Samuel R. Buss,et al.  Small Stone in Pool , 2014, Log. Methods Comput. Sci..

[20]  Adnan Darwiche,et al.  On the power of clause-learning SAT solvers as resolution engines , 2011, Artif. Intell..

[21]  Eli Ben-Sasson,et al.  Size space tradeoffs for resolution , 2002, STOC '02.

[22]  Albert Atserias,et al.  Narrow Proofs May Be Maximally Long , 2014, Computational Complexity Conference.

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

[24]  Marc Vinyals,et al.  CNFgen: A Generator of Crafted Benchmarks , 2017, SAT.

[25]  Joao Marques-Silva,et al.  Empirical Study of the Anatomy of Modern Sat Solvers , 2011, SAT.

[26]  Gilles Audemard,et al.  Refining Restarts Strategies for SAT and UNSAT , 2012, CP.

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

[28]  Samuel R. Buss,et al.  Improved Separations of Regular Resolution from Clause Learning Proof Systems , 2012, J. Artif. Intell. Res..

[29]  Stanislav Zivny,et al.  Relating Proof Complexity Measures and Practical Hardness of SAT , 2012, CP.

[30]  Albert Atserias,et al.  A combinatorial characterization of resolution width , 2008, J. Comput. Syst. Sci..

[31]  Eli Ben-Sasson,et al.  Near Optimal Separation Of Tree-Like And General Resolution , 2004, Comb..

[32]  Armin Biere,et al.  Evaluating CDCL Variable Scoring Schemes , 2015, SAT.

[33]  Michael Alekhnovich,et al.  Resolution Is Not Automatizable Unless W[P] Is Tractable , 2008, SIAM J. Comput..

[34]  James M. Crawford,et al.  Experimental Results on the Crossover Point in Random 3-SAT , 1996, Artif. Intell..

[35]  Alasdair Urquhart,et al.  Formal Languages]: Mathematical Logic--mechanical theorem proving , 2022 .

[36]  Eli Ben-Sasson,et al.  Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[37]  Jacobo Torán,et al.  Space Bounds for Resolution , 1999, STACS.

[38]  Jakob Nordström On the interplay between proof complexity and SAT solving , 2015, SIGL.

[39]  Russell Impagliazzo,et al.  Time-Space Trade-offs in Resolution: Superpolynomial Lower Bounds for Superlinear Space , 2016, SIAM J. Comput..

[40]  Endre Szemerédi,et al.  Many hard examples for resolution , 1988, JACM.

[41]  Gilles Audemard,et al.  Predicting Learnt Clauses Quality in Modern SAT Solvers , 2009, IJCAI.

[42]  Michael Alekhnovich,et al.  Space Complexity in Propositional Calculus , 2002, SIAM J. Comput..

[43]  Armin Biere,et al.  Evaluating CDCL Restart Schemes , 2018, POS@SAT.

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

[45]  Gunnar Stålmarck Short resolution proofs for a sequence of tricky formulas , 2009, Acta Informatica.

[46]  Michael Alekhnovich,et al.  An Exponential Separation between Regular and General Resolution , 2007, Theory Comput..