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
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.
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.
Abstract: Validation of an automation system is an important issue. The goal is to check if the system under investigation, modeled by a Petri net, never enters the undesired states. Usually, tools dedicated to Petri nets such as DESIGN/CPN are used to make reachability analysis. The biggest problem with this approach is that it is impossible to generate the full occurence graph of the system because it is too large. In this paper, we show how computational methods such as temporal logic model checking and Groebner bases can be used to verify the correctness of the design of an automation system. We report our experimental results with two automation systems: the Automated Guided Vehicle (AGV) system and the traffic light system. Validation of these two systems ranged from 10 to 30 seconds on a PC depending on the optimizing parameters.