Some Properties of Pigeon-Hole Formulas
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    Abstract:

    The pigeon-hole formula PHnn+1, defined from the pigeon hole principles, is one of the hardest examples on resolution. The research of the formula’s constructions and properties is helpful for constructing other hard examples. It is shown that PHnn+1 is a minimal unsatisfiable formula. The two normal forms of maximal satisfiable truth assignments for PHnn+1 are presented by the minimal unsatisfiability of PHnn+1, which one of normal forms is used in Haken’s proof of hardness for PHnn+1. The formula PHnn+1 has well isomorphics properties on substructures. For the modified DPLL algorithm introduced by the isomorphism rule, the complexity of refutation proof of PHnn+1 can be reduced to O(n3).

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许道云,韦立,王晓峰.鸽巢公式的一些性质.软件学报,2011,22(11):2553-2563

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  • Received:July 07,2010
  • Revised:November 03,2010
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