On Polynomial Ideals, Their Complexity, and Applications
نویسنده
چکیده
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.
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