Towards an Efficient Tableau Method for Boolean Circuit Satisfiability Checking
Boolean circuits offer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a tableau method for solving satisfiability problems for Boolean circuits is devised. The method employs a direct cut rule combined with deterministic deduction rules. Simplification rules for circuits and a search heuristic attempting to minimize the search space are developed. Experiments in symbolic model checking domain indicate that the method is competitive against state-of-the-art satisfiability checking techniques and a promising basis for further work.
KeywordsBoolean Function Conjunctive Normal Form Symbolic Model Check Boolean Circuit Input Gate
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- 2.A. Biere, A. Cimatti, E. M. Clarke, M. Fujita, and Y. Zhu. Symbolic model checking using SAT procedures instead of BDDs. In Proceedings of the 36th ACM/IEEE Design Automation Conference (DAC’99), pages 317–320. ACM, 1999.Google Scholar
- 3.A. Biere, E. Clarke, R. Raimi, and Y. Zhu. Verifying safety properties of a PowerPC microprocessor using symbolic model checking without BDDs. In N. Halbwachs and D. Peled, editors, Computer Aided Verification: 11th International Conference (CAV’99), volume 1633 of LNCS, pages 60–71. Springer, 1999.Google Scholar
- 4.A. Borälv. The industrial success of verification tools based on Stålmarck’s method. In Proceeding of the 9th International Conference on Computer Aided Verification (CAV’97), volume 1254 of LNCS, pages 7–10, Haifa, Israel, June 1997. Springer.Google Scholar
- 8.L. Guerra e Silva, L. M. Silveira, and J. Marques-Silva. Algorithms for solving Boolean satisfiability in combinatorial circuits. In Design, Automation and Test in Europe (DATE’99), pages 526–530. IEEE, 1999.Google Scholar
- 9.T. Junttila. BCSat — a satisfiability checker for Boolean circuits. Available at http://www.tcs.hut.fi/~tjunttil/bcsat.
- 10.H. Kautz, D. McAllester, and B. Selman. Exploiting variable dependency in local search. A draft available at http://www.cs.cornell.edu/home/selman/papers-ftp/papers.html, 1997.
- 11.H. Kautz and B. Selman. Pushing the envelope: Planning, propositional logic, and stochastic search. In Proceedings of the 13th National Conference on Artificial Intelligence, Portland, Oregon, July 1996.Google Scholar
- 13.F. Massacci. Simplification — a general constraint propagation technique for propositional and modal tableaux. In H. de Swart, editor, Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX-98), pages 217–231. Springer, May 1998.Google Scholar
- 14.A. Nerode and R. A. Shore. Logic for Applications. Text and Monographs in Computer Science. Springer-Verlag, 1993.Google Scholar
- 15.I. Niemelä and P. Simons. Efficient implementation of the well-founded and stable model semantics. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289–303. The MIT Press, 1996.Google Scholar
- 16.C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1995.Google Scholar
- 19.H. Zhang. SATO: An efficient propositional prover. In Automated Deduction-CADE-14, volume 1249 of LNCS, pages 272–275. Springer, 1997.Google Scholar