Abstract

A polynomial ideal membership problem is a (w+1)-tuple P=(f, g 1 ,g 2 , ..., g w ) where f and the g i are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g i . For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets.KeywordsWord ProblemTotal DegreePolynomial IdealCommutative SemigroupReachability ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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