Average time complexity of the SAT 1.2 algorithm

  • Jun Gu
  • Qian-Ping Gu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 834)


In this paper, we give an efficient algorithm, the SAT1.2 algorithm, for the SAT problem. For randomly generated formulas with n clauses, m variables, and l literals per clause, the average run time of the SAT1.2 algorithm is O(mo(1)n2) for l≥3 and n/mα2l/l, where α<l is a constant. Real algorithm executions indicate that the SAT1.2 algorithm is much more efficient than the well known Davis-Putnam algorithm for certain classes of CNF formulas with small l. This is important in practice, since for large l, most vectors in {0, 1}m are the solutions of the problem. Thus, a random exhaustive search can efficiently solve the problem. The SAT1.2 algorithm can find a solution for a satisfiable CNF formula efficiently but gives an answer in O(mo(1)2m) time to an unsatisfiable CNF formula. 3


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jun Gu
    • 1
  • Qian-Ping Gu
    • 2
  1. 1.Dept. of Electrical and Computer EngineeringUniv. of CalgaryCalgaryCanada
  2. 2.Dept. of Computer SoftwareThe Univ. of AizuFukushimaJapan

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