Symbolic model checking using algebraic geometry
In this paper, I show that methods from computational algebraic geometry 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 Ordered 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.
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- 1.W. W. Adams and P. Loustaunau. An Introduction to Gröbner Bases, Volume 3 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1994.Google Scholar
- 2.D. Bayer and M. Stillman. Macaulay: A System for Computation in Algebraic Geometry and Commutative Algebra. Source and object code available for Unix and Macintosh computers. Contact the authors, or download from math. harvard. edu via anonymous ftp., 1982–1994.Google Scholar
- 4.T. Becker and V. Weispfenning. Gröbner Bases, Volume 141 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1993.Google Scholar
- 6.B. Buchberger. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, University of Innsbruck, 1965.Google Scholar
- 7.B. Buchberger. Gröbner bases: An algorithmic method in polynomial ideal theory. In N. K. Bose, editor, Multidimensional Systems Theory, pages 184–232. D. Reidel, 1985.Google Scholar
- 8.J. Burch, E. Clarke, K. McMillan, D. Dill, and L. Hwang. Symbolic model checking: 1020 states and beyond. In Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science, pages 428–439, 1990.Google Scholar
- 9.D. Cox, J. Little, and D. O'Shea. Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1992.Google Scholar
- 11.R. Hartshorne. Algebraic Geometry, Volume 52 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1977.Google Scholar
- 12.E. Mayr and A. Meyer. The complexity of the word problem for commutative semigroups and polynomial ideals. Adv. in Math., 1982.Google Scholar
- 13.K. L. McMillan. Symbolic Model Checking. Kluwer Academic Publishers, Boston, 1993.Google Scholar