Groebner Bases Computation in Boolean Rings is P-SPACE

The theory of Groebner Bases, which has recently been honored with the ACM Paris Kanellakis Theory and Practice Award, has become a crucial building block to computer algebra, and is widely used in science, engineering, and computer science. It is wellknown that Groebner bases computation is EXP-SPACE in a general polynomial ring setting. However, for many important applications in computer science such as satisfiability and automated verification of hardware and software, computations are performed in a Boolean ring. In this paper, we give an algorithm to show that Groebner bases computation is PSPACE in Boolean rings. We also show that with this discovery, the Groebner bases method can theoretically be as efficient as other methods for automated verification of hardware and software. Additionally, many useful and interesting properties of Groebner bases including the ability to efficiently convert the bases for different orders of variables making Groebner bases a promising method in automated verification. Keywords—Algorithm, Complexity, Groebner basis, Applications of Computer Science.