An average case analysis of Monien and Speckenmeyer's mechanical theorem proving algorithm

  • T. H. Hu
  • C. Y. Tang
  • R. C. T. Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 557)


In this paper, we shall give an average case analysis of a mechanical theorem proving algorithm based upon branching techniques for solving the k-satisfiability problem. The branching algorithm is a modified version of Monien and Speckenmeyer's branching algorithm [Monien and Speckenmeyer 1985]. Monien and Speckenmeyer's branching algorithm has a worst case time complexity which is strictly better than 2n [Monien and Speckenmeyer 1985]. Based upon the probability distribution model that given r clauses, each clause is randomly chosen from the set of all k-literal clauses over n variables and each clause is chosen independently with others, we can show that our branching algorithm runs in exponential expected time under the condition that \(\mathop {\lim }\limits_{r,n \to \infty } \frac{t}{n} \to \infty\) and k is a constant.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • T. H. Hu
    • 1
  • C. Y. Tang
    • 1
  • R. C. T. Lee
    • 2
    • 3
  1. 1.Institute of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan, Republic of China
  2. 2.National Tsing Hua UniversityHsinchuTaiwan
  3. 3.Academia Sinica TaipeiTaiwan, Republic of China

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