Abstract
Some elementary concepts on Equational Theories and Rewriting Systems are introduced, followed by a brief review on the main ideas of the Knuth-Bendix completion procedure. Then a formalization of Petri Nets as Term Rewriting Systems is proposed, which allows the use of rewriting techniques for studying the behaviour of general deterministic Petri Nets. Particularly the simplification of Term Rewriting Systems obtained formalizing Petri Nets proves to be a powerful method to obtain an efficient system for detecting deadlock situations.
Experiments have been carried out using KBLab, an Automated Theorem Prover for equational theories based on the Knuth-Bendix algorithm.
KBLab has been developed at the Computer Science Department of the University of Milan, as part of the CNR Project “Sistemi informatici e Calcolo Parallelo”.
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References
L. Bachmair, N. Dershowitz, J. Hsiang, 1986, Orderings for equational proofs, in Proceedings 1st Annual IEEE Symp. on Logic in Computer Science, Cambridge, MA, pp. 346-357.
B. Buchberger, R. Loos, 1983, Algebraic simplification, in Computer Algebra: Symbolic and Algebraic Computation, Springer Verlag, Wien.
N. Dershowitz, 1982, Orderings for term rewriting systems, J. of Theoretical Computer Science 17, pp. 279–301.
N. Dershowitz, 1989, Completion and its applications, in Resolution of Equations in Algebraic Structures, pp. 31-48.
J. Hsiang, M. Rusinovitch, 1987, On word problems in equational theories, Proceedings 14th Int. Conf. on Automata Languages and Programming, Karlsrhue.
J.M. Hullot, 1980, A catalogue of canonical term rewriting systems, Rept. CSL-113, SRI International, Menlo Park, CA.
D.E. Knuth, P. Bendix, 1970, Simple word problems in universal algebras”, Proceedings of the Conf. on Computational Problems in Abstract Algebras, Pergamon Press, pp. 263-298.
A. Paccanaro, 1991, KBLAb 1.7: user manual, Technical Report, Department of Computer Science, University of Milan.
J.L. Peterson, 1981, Petri Net Theory and the Modeling of Systems, Prentice Hall, Englewood Cliffs, N.J.
W. Reising, 1985, Petri Nets: An Introduction, Springer-Verlag, Berlin-New York
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© 1994 Springer Science+Business Media New York
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Paccanaro, A. (1994). Studying the Behaviour of Petri Nets through a Formalization as Term Rewriting Systems. In: Baeza-Yates, R. (eds) Computer Science 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9805-0_37
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DOI: https://doi.org/10.1007/978-1-4757-9805-0_37
Publisher Name: Springer, Boston, MA
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