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Some hard examples for the resolution method

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Abstract

Givenn propositional variables, letK n (i, j), 0≤i≤j≤n, be the set (or disjunction) of all conjunctions ofi literals of which exactlyj literals are negative. Dunham and Wang conjectured that it may require exponential time to decide that every disjunctionK n (i, j) is not valid by the resolution method. This paper gives a proof of the conjecture and then exhibits a new counterexample to the feasibility of the resolution or consensus method.

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References

  1. Brariford Dunham and Hao Wang, Towards feasible solution of the tautology problem, Ann. Math. Logic,10 (1976), 117–154.

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  1. Yu Xiangdong

    Present address: Department of Computer Science, Columbia University in the City of New York, New York, USA

Authors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan

    Yu Xiangdong

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  1. Yu Xiangdong
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Yu, X. Some hard examples for the resolution method. J. of Comput. Sci. & Technol. 5, 302–304 (1990). https://doi.org/10.1007/BF02945319

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  • DOI: https://doi.org/10.1007/BF02945319

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