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  The search efficiency of theorem proving strategies: an analytical comparison

Plaisted, D.(1994). The search efficiency of theorem proving strategies: an analytical comparison (MPI-I-94-233). Saarbrücken: Max-Planck-Institut für Informatik.

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MPI-I-94-233.pdf (Any fulltext), 343KB
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Plaisted, David1, Author           
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1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 Abstract: We analyze the search efficiency of a number of common refutational theorem proving strategies for first-order logic. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of exponential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to propositional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strategy which is of interest for term-rewriting based theorem proving is the A-ordering strategy, and we discuss it in some detail. We show some advantages of A-ordering over other strategies, which may help to explain its efficiency in practice. We also point out some of its combinatorial inefficiencies, especially in relation to goal-sensitivity and irrelevant clauses. In addition, SLD-resolution, which is of importance for Prolog implementation, has combinatorial inefficiencies; this may suggest basing Prolog implementations on a different theorem proving strategy.

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Language(s): eng - English
 Dates: 1994
 Publication Status: Issued
 Pages: 40 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/94-233
Report Nr.: MPI-I-94-233
BibTex Citekey: Plaisted94b
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Title: Research Report / Max-Planck-Institut für Informatik
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