Abstract
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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Hu, T.H., Tang, C.Y., Lee, R.C.T. (1991). An average case analysis of Monien and Speckenmeyer's mechanical theorem proving algorithm. In: Hsu, WL., Lee, R.C.T. (eds) ISA'91 Algorithms. ISA 1991. Lecture Notes in Computer Science, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54945-5_55
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DOI: https://doi.org/10.1007/3-540-54945-5_55
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