Solving SAT by algorithm transform of Wu’s method
Recently algorithms for solving propositional satisfiability problem, or SAT, have aroused great interest, and more attention has been paid to transformation problem solving. The commonly used transformation is representation transform, but since its intermediate computing procedure is a black box from the viewpoint of the original problem, this approach has many limitations. In this paper, a new approach called algorithm transform is proposed and applied to solving SAT by Wu’s method, a general algorithm for solving polynomial equations. By establishing the correspondence between the primitive operation in Wu’s method and clause resolution in SAT, it is shown that Wu’s method, when used for solving SAT, is primarily a restricted clause resolution procedure. While Wu’s method introduces entirely new concepts, e.g. characteristic set of clauses, to resolution procedure, the complexity result of resolution procedure suggests an exponential lower bound to Wu’s method for solving general polynomial equations. Moreover, this algorithm transform can help achieve a more efficient implementation of Wu’s method since it can avoid the complex manipulation of polynomials and can make the best use of domain specific knowledge.
Keywordsalgorithm design satisfiability problem Wu’s method automated reasoning
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- Kapur D, Kakshman Y N. Elimination Theory: An Introduction. Chapter 2 in Symbolic and Numerical Computation for Artificial Intelligence, Academic Press, 1992.Google Scholar
- He Simin. The Design and Analysis of Algorithms for Satisfiability Problem. Ph.D. dissertation, Department of Computer Science and Technology, Tsinghua University, 1997.Google Scholar
- Kapur D, Narendran P. An equational approach to theorem proving in first-order predicate calculus. InProceedings of the Ninth International Joint Conference on Aetificial Intelligence (IJCAI-85), Los Angeles, California, 1985, pp.1146–1153.Google Scholar
- Wos L. Automated Reasoning: 33 Basic Research Problems. Prentice Hall, 1988.Google Scholar
- Mitchell D, Selman B, Levesque H. Hard and easy distribution of SAT problems. InProceedings of the Tenth National Conference on Artificial Intelligence (AAAI-92), San Jose, CA, July 1992, pp.459–465.Google Scholar
- Selman B, Levesque H, Mitchell D. A new method for solving hard satisfiability problems. InProceedings of AAAI-92, San Jose, CA, July 1992, pp. 440–446.Google Scholar