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Persistent and Quasi-Persistent Lemmas in Propositional Model Elimination

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Abstract

Model elimination is a back-chaining strategy to search for and construct resolution refutations. Recent extensions to model elimination, implemented in Modoc, have made it a practical tool for satisfiability checking, particularly for problems with known goals. Many formulas can be refuted more succinctly by recording certain derived clauses, called lemmas. Lemmas can be used where a clause of the original formula would normally be required. However, recording too many lemmas overwhelms the proof search. Lemma management has a significant effect on the performance of Modoc. Earlier research studied pure persistent (global) strategies, and pure unit-lemma (local) strategies. This paper describes and evaluates a hybrid strategy to control the lifetime of lemmas, as well as a new technique for deriving certain lemmas efficiently, using a lazy strategy. Unit lemmas are recorded locally as in previous practice, but certain lemmas that are considered valuable are asserted globally. A range of functions for estimating value is studied experimentally. Criteria are reported that appear to be suitable for a wide range of application-derived formulas.

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Authors and Affiliations

  1. Electronics for Imaging, 303 Velocity Way, Foster City, CA, 94404, USA

    Fumiaki Okushi

  2. Department of Computer Science, SOE, University of California, Santa Cruz, CA, 95064, USA

    Allen Van Gelder

Authors
  1. Fumiaki Okushi
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  2. Allen Van Gelder
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Okushi, F., Van Gelder, A. Persistent and Quasi-Persistent Lemmas in Propositional Model Elimination. Annals of Mathematics and Artificial Intelligence 40, 373–401 (2004). https://doi.org/10.1023/B:AMAI.0000012873.60775.ba

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