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33 Basic Test Problems: A Practical Evaluation of Some Paramodulation Strategies
, 1996
"... Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "ou ..."
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Cited by 24 (5 self)
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Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easytofind proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ
DoubleExponential Complexity of Computing a Complete Set of ACUnifiers
 In Proceedings 7th IEEE Symposium on Logic in Computer Science
"... A new algorithm for computing a complete set of unifiers for two terms involving associativecommutative function symbols is presented. The algorithm is based on a nondeterministic algorithm given by the authors in 1986 to show the NPcompleteness of associativecommutative unifiability. The algori ..."
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Cited by 18 (0 self)
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A new algorithm for computing a complete set of unifiers for two terms involving associativecommutative function symbols is presented. The algorithm is based on a nondeterministic algorithm given by the authors in 1986 to show the NPcompleteness of associativecommutative unifiability. The algorithm is easy to understand, its termination can be easily established. More importantly, its complexity can be easily analyzed and is shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a doubleexponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associativecommutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense. This is the first associativecommutative unification algorithm whose complexity has been completely analyzed. The approach can also be used to show a singl...