Project Description Since Hilbert’s seminal works on invariant theory, which laid foundational results for modern commutative algebra and algebraic geometry, and Mumford’s seminal work on geometric invariant theory, much progress has been made on the computational aspects of invariant theory. Despite all of the progress made in this past century, many open questions still remain on the efficient computation of a generating set (or of a separating set) of invariant polynomials. The goal of this project is to make progress in efficiently computing a generating set of invariant polynomials for special group actions, which have profound applications in fundamental theoretical problems in computer science.