Abstract

In this paper, we present an optimal, exponential space algorithm for generating the reduced Grobner basis of binomial ideals. We make use of the close relationship between commutative semigroups and pure difierence binomial ideals. Based on an optimal al- gorithm for the uniform word problem in commutative semigroups, we flrst derive an exponential space algorithm for constructing the reduced Grobner basis of pure difier- ence binomial ideals. In addition to some applications to flnitely presented commutative semigroups, this algorithm is then extended to an exponential space algorithm for gen- erating the reduced Grobner basis of binomial ideals over Q in general.

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