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In ComputerAided Verification, CAV '96 (Rajeev Alur and Thomas A. Henzinger, eds.), LNCS vol. 1102, 1991, 26--37, c flSpringerVerlag

Summary: In Computer­Aided Verification, CAV '96 (Rajeev Alur and Thomas A. Henzinger, eds.), LNCS vol. 1102, 1991, 26--37, c
Symbolic Model Checking Using Algebraic Geometry
George S. Avrunin
Department of Mathematics, University of Massachusetts, Amherst, MA 01003­4515
Abstract. In this paper, I show that methods from computational algebraic ge­
ometry can be used to carry out symbolic model checking using an encoding of
Boolean sets as the common zeros of sets of polynomials. This approach could
serve as a useful supplement to symbolic model checking methods based on Or­
dered Binary Decision Diagrams and may provide important theoretical insights
by bringing the powerful mathematical machinery of algebraic geometry to bear
on the model checking problem.
1 Introduction
Symbolic model checking [8, 13] with Ordered Binary Decision Diagrams (OBDDs),
or variants of OBDDs, is a widely used and successful technique for verifying properties
of concurrent systems, both hardware and software. But there are many systems for
which the OBDDs are too large to make model checking feasible and, aside from a few
results like McMillan's theorem on bounded width circuits [13] or Bryant's theorem on
integer multiplication [5], there is little theoretical guidance to indicate precisely when


Source: Avrunin, George S. - Department of Mathematics and Statistics, University of Massachusetts at Amherst
Kalla, Priyank - Department of Electrical and Computer Engineering, University of Utah


Collections: Engineering; Mathematics