Abstract
In order to improve the efficiency of the Knuth-Bendix Algorithm by eliminating unnecessary reductions, a criterion predicting confluence of critical pairs was given by Winkler in 1983. Subsequently, Winkler and Buchberger also presented a more general form of Newman's Lemma. We derive a more general confluence criterion directly from the Generalised Newman Lemma and integrate it into the Knuth-Bendix Algorithm with the aim of generating fewer critical pairs. With the new criterion it is possible to give a concise justification for the removal of reducible rules in the KB-algorithm. A slightly specialised version of this criterion needs only a single match to test for; empirical results substantiate the claim of a considerable gain in efficiency for the Knuth-Bendix Algorithm.
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References
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© 1985 Springer-Verlag Berlin Heidelberg
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Küchlin, W. (1985). A confluence criterion based on the generalised Newman Lemma. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_294
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DOI: https://doi.org/10.1007/3-540-15984-3_294
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