Resolution and Satisfiability Algorithms - Reading Course

Potential reading lists, (More suggestions welcomed.)

Background on resolution.

S. Buss, "Introduction to Proof Theory", from Handbook of Proof Theory, pp. 1-78, Elsevier-North Holland, 1998. Section 1.3, pages 18-26, is an introduction to resolution theorem proving that can be read largely independently of the earlier material in this article.

P. Beame and T. Pitassi, Propositional Proof Complexity: Past, Present and Future, in Current Trends in Theoretical Computer Science Entering the 21st Century, World Scientific, 2001, pp 42-70.  Also ECCC TR98-067.  Survey article about propositional proof complexity in general (not just resolution).

A. Nadel,  Backtrack Search Algorithms for Propositional Logic Satisfiability: Review and Innovations, Masters Thesis, Haifa, 2002. Has a survey of DPLL search methods in addition to describing his Jerusat SAT solver. Associated web site at

Algorithms for Finding Satisfying Assignments.

J. Marques Silva, K. Sakallah, GRASP - A New Search Algorithm for Satisfiability, Intl. Conf. on Computer Aided Design, ICCAD'96 M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, S. Malik.

M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, S. Malik, Chaff: Engineering an Efficient SAT Solver., Proc. Design Automation Conference (DAC) 2001.

Z. Fu, Y. Mahajan, S. Malik, "New Features of the SAT'04 versions of zChaff."

L. Zhang, C.F. Madigan, M.H. Moskewicz, S. Malik, Efficient conflict driven learning in a Boolean satisfiability solver. in ICCAD, 2001, pp. 279-285.

zChaff web site,, with source code. 2004.

E. Goldberg, Yakov Novikov, BerkMin: A Fast and Robust Sat-Solver, Design Automation and Test in Europe (DATE) 2002.

A. Nadel, Backtrack Search Algorithms for Propositional Logic Satisfiability: Review and Innovations, Masters Thesis, Haifa, 2002. Jerusat SAT solver, and a review of the state of the art in 2002. Associated web site at

J. Marques Silva, The Impact of Branching Qeuristics in Propositional Satisfiability Algorithms, Progress in Artificial Intelligence, 9th Portuguese Conference on Artificial Intelligence, EPIA'99, 1999, LNCS 1695, 1999.

L. Zhang, S. Malik, The Quest for Efficient Boolean Satisfiability Solvers, CADE 2002 and CAV 2002. A Survey of GRASP-Chaff-BerkMin and other algorithms.

B. Selman, H. Levesque, D. Mitchell, A New Method for Solving Hard Satisfiability Problems. 10th National Conf. on Artificial Intelligence (AAAI-92), 440-446. GSAT algorithm.

B. Selman, H. Kautz, B. Cohen, Local Search Strategies for Satisfiability Testing, in Cliques, Coloring, and Satisfiability (DIMACS '93). WalkSAT (a.k.a.Stochastic Local Search -- SLS -- for Satisfiability). Web page with source code at

A. Braunstein, M Mezard, R. Zecchina, Survey Propagation: An Algorithm for Satisfiability, Random Structures and Algorithms, 27(2), 2005, 201-226. Journal page link.

J. Yedida, W. Freeman, Yair Weiss, Understanding Belief Propagation and it Generalizations, IJCAI'2001 (No direct discussion of SAT algorithms.)

R. Paturi, P. Pudlák, F. Zane, "Satisfiability Coding Lemma ", in FOCS'97, pp 566-574. and Chicago Journal of Theoretical Computer Science 1999..

R. Paturi, P. Pudlák, M. Saks, F. Zane, "An Improved Exponential-time Algorithm for k-SAT", in FOCS'98, pp 628-637. and J. ACM 52 (2005) 337-364.

R. Impagliazzo, R. Paturi, F. Zane, Which Problems Have Strongly Exponential Complexity?, JCSS 63(4), 2001, pp 512-530.

R. Impagliazzo, R. Paturi, On the Complexity of k-SAT, JCSS 62(3), 2001, pp 367-375.

K. Iwama, S. Tamaki, "Improved Upper Bounds for 3-SAT", ECCC, 2003.

D. Rolf, Improved Bound for the PPSZ/Schoning Algorithm for 3_SAT, ECCC, 2005.

U. Schöning, "A Probabilitistic Algorithm for k-SAT and Constraint Satisfaction Problems", in FOCS'99, pp. 410-414. (Conference version of next paper.)

U. Schöning, "A Probabilistic Algorithm for k-SAT based on limited local search and restart". Algorithmica 32 (2002) 615-623.

T. Hofmeister, U. Schöning, R. Schuler, O. Watanabe, "A probabilistic 3-SAT algorithm further improved'', 19th Symposium on Theoretical Aspects of Computer Science (STACS), LNCS 2285: 192-202, 2002.

S. Baumer, R. Schuler, "Improving a probabilistic 3-SAT Algorithm by Dynamic Search and Independent Clause Pairs''., Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT 2003)

E. Dantsin, A. Goerdt, E. Hirsch, R. Kannan, J. Kleinberg, C. Papadimitriou, P. Raghavan, U. Schoning, "A determinististic 2(2-2/(k+1))^n algorithm for k-SAT based on local search", Theoretical Computer Science 289 (2002) 69-83.

T. Greuggemann and W. Kern, "An improved local search algorithm for 3-SAT", Tech. Rep, Univ. of Twente, Jan 2004.

R. Schuler, "An algorithm for the satisfiability problem of formulas in conjunctive normal form", J. of Algorithms, 54 (2005) 40-44.

E. Dantzin, A. Wolpert, "Derandomization of Schuler's algorithm for SAT", ECCC 2004.

P. Beame, R. Impagliazzo, T. Pitassi, N. Segerlind, "Memoization and DPLL: Formula Caching Proof Systems, Proc. CCC'2003. (The version online here has some corrections applied from the version that appeared in CCC'03.)

P. Beame, H. Kautz, A. Sabharwal, "Understanding the Power of Clause Learning." IJCAI'2003. Expanded journal version: Towards Understanding and Harnessing the Power of Clause Learning, J. Artificial Intelligence Research, 2004, 22, 319-351.

M. Sheeran and G. Stalmarck. A tutorial on Stalmarck's proof procedure for propositional logic. 2nd Intl Conf on Formal Methods in Computer-Aided Design (FMCAD) 1998, LNCS 1551, Springer-Verlag, pp. 82-99.

E. Dantsin, E. Hirsch, A. Wolpert.Algorithms for SAT based on Search in Hamming Balls, STACS 2004, LNCS 2996, pp. 141-151. Hamming ball method for unrestricted SAT.

B Aspvall, M. Plass, R. Tarjan, A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas, Information Processing Letters, vol 8, no. 3 (1979) 121-123.

Structural Results

E. Friedgut, J. Bourgain, Sharp Tresholds of Graph Properties and the k-SAT Problem, J.AMS, 12 (1999) 1017-1054.

K. Xu and W. Li,  The SAT Phase Transition, Science in China, Series E, 1999.

SAT Solver Competition Results

International SAT Competitions Web Page at