论文信息 - On resolution with short clauses

On resolution with short clauses

AbstractWe investigate properties ofk-resolution, a restricted version of resolution in which one parent clause must have length at mostk. Starting from a unit-preference strategy, we compare minimal proof lengths of unit-resolution and unrestricted resolution. In particular, we show that the speed-up by using resolution is bound by $$\sqrt t $$ if the shortest unit-resolution refutation needst steps. Next we present an algorithm which decides whether the empty clause can be deduced by 2-resolution from a formula Φ and has time complexity O(length(Φ)4). Finally we describe effects onk-resolution if a formula is transformed intot-CNF and show that extended 3-resolution is complete and sound.

Hans Kleine Büning | Michael Buro

[1] Jean H. Gallier,et al. Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[2] Armin Haken,et al. The Intractability of Resolution , 1985, Theor. Comput. Sci..

[3] L. Wos,et al. The unit preference strategy in theorem proving , 1899, AFIPS '64 (Fall, part I).

[4] Maria Grazia Scutellà,et al. Polynomially Solvable Satisfiability Problems , 1988, Inf. Process. Lett..

[5] Elmar Eder,et al. Relative complexities of first order calculi , 1992, Artificial intelligence = Künstliche Intelligenz.

[6] Hans Kleine Büning. On generalized Horn formulas and k-resolution , 1993, Theor. Comput. Sci..

[7] Shuji Doshita,et al. The Satisfiability Problem for a Class Consisting of Horn Sentences and Some Non-Horn Sentences in Proportional Logic , 1983, Inf. Control..