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Buchberger's algorithm: a constraint-based completion procedure

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Bachmair,  Leo
Programming Logics, MPI for Informatics, Max Planck Society;

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Ganzinger,  Harald
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Bachmair, L., & Ganzinger, H. (1994). Buchberger's algorithm: a constraint-based completion procedure. In J.-P. Jouannaud (Ed.), Proceedings of the 1st International Conference on Constraints in Computational Logics (CCL'94) (pp. 285-301). Berlin, Germany: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-AD63-C
Abstract
We present an extended completion procedure with built-in theories defined by a collection of associativity and commutativity axioms and additional ground equations, and reformulate Buchberger's algorithm for constructing Gr\"obner 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.