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An average case analysis of a resolution principle algorithm in mechanical theorem proving

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Abstract

The satisfiability problem is a well known NP-complete problem. In artificial intelligence, solving the satisfiability problem is called mechanical theorem proving. One of those mechanical theorem proving methods is the resolution principle which was invented by J.R. Robinson. In this paper, we shall show how an algorithm based upon the resolution principle can be analyzed. Letn andr 0 denote the numbers of variables and input clauses respectively. LetP 0 denote the probability that a variable appears positively, or negatively, in a clause. Our analysis shows that the expected total number of clauses processed by our algorithm isO(n+r 0) ifP 0 is a constant,r 0 is polynomially related withn, andn is large.

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Authors and Affiliations

  1. Institute of Computer Science, National Tsing Hua University, 30043, Hsinchu, Taiwan, Republic of China

    T. H. Hu & C. Y. Tang

  2. National Tsing Hua University, 30043, Hsinchu, Taiwan

    R. C. T. Lee

  3. Academia Sinica, Taipei, Taiwan, Republic of China

    R. C. T. Lee

Authors
  1. T. H. Hu
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  2. C. Y. Tang
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  3. R. C. T. Lee
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Additional information

This research was supported partially by the National Science Council of the Republic of China under the Grant NSC 78-0408-E007-06.

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Hu, T.H., Tang, C.Y. & Lee, R.C.T. An average case analysis of a resolution principle algorithm in mechanical theorem proving. Ann Math Artif Intell 6, 235–251 (1992). https://doi.org/10.1007/BF01531030

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