Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals

Abstract: In this paper, we give decision criteria for normal binomial difference polynomial ideals in the univariate difference polynomial ring F{y} to have finite difference Groebner bases and an algorithm to compute the finite difference Groebner bases if these criteria are satisfied. The novelty of these criteria lies in the fact that complicated properties about difference polynomial ideals are reduced to elementary properties of univariate polynomials in Z[x].