Homomorphism Proof Systems for Unsatisfiable Formulas
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    Abstract:

    A homomorphism φ of CNF formulas from H to F is a function mapping the set of literals in H to the set of literals in F and it preserves complements and clauses. If the formula H is homomorphic to the formula F, then the unsatisfiability of H implies the unsatisfiability of F. A CNF formula F is minimally unsatisfiable if F is unsatisfiable and the resulting formula deleting any one clause from F is satisfiable. MU(1) is a class of minimally unsatisfiable formulas with the deficiency of the number of clauses and variables to be one. A triple (H,φ,F) is called a homomorphism proof from H of F if φ is a homomorphism from H to F. In this paper, a method from the basic matrix of MU(1) formula is used to prove that a tree resolution proof for an unsatisfiable formula F can be transformed into a homomorphism proof from a MU(1) formula for F. Whence, the homomorphism proof system from formulas in MU(1) is complete, and this proof system and the tree resolution proof system can be transformed mutually in polynomial time on the size of proof.

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许道云.不可满足公式的同态证明系统.软件学报,2005,16(3):336-345

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  • Received:August 29,2003
  • Revised:October 09,2004
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