Abstract: 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
setting. In this paper, we give an algorithm to show that Groebner
bases computation is P-SPACE 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.