Abstract
We present an extended completion procedure with builtin theories defined by a collection of associativity and commutativity axioms and additional ground equations, and reformulate Buchberger's algorithm for constructing Gröbner bases for polynomial ideals in this formalism. The presentation of completion is at an abstract level, by transition rules, with a suitable notion of fairness used to characterize a wide class of correct completion procedures, among them Buchberger's original algorithm for polynomial rings over a field.
The research described in this paper was supported in part by the German Science Foundation (Deutsche Forschungsgemeinschaft) under grant Ga 261/4-1, by the German Ministry for Research and Technology (Bundesministerium für Forschung und Technologie) under grant ITS 9102/ITS 9103, by the ESPRIT Basic Research Working Group 6028 (Construction of Computational Logics), and by the National Science Foundation under grant INT-9314412. The first author was also supported by the Alexander von Humboldt Foundation.
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Bachmair, L., Ganzinger, H. (1994). Buchberger's algorithm: A constraint-based completion procedure. In: Jouannaud, JP. (eds) Constraints in Computational Logics. CCL 1994. Lecture Notes in Computer Science, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016860
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DOI: https://doi.org/10.1007/BFb0016860
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