Abstract
It is shown that each live and safe free-choice system without frozen token can be reduced either to a live and safe marked T-graph (marked graph) or to a live and safe marked P-graph (state machine). The four proposed reduction rules are purely local and preserve the behavioural properties in both directions. Hence the method can be used for both, effective analysis and correct design.
The class of systems which can be reduced to marked P-graphs (T-graphs, respectively) can be characterized without using the reduction rules by their P- and T-components. The two classes are not disjoint; systems in the intersection of the classes can be reduced to a unique systems with only two elements.
Work supported partly by the Esprit Basic Research Action No. 3148: DEMON.
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References
Andre, C.: Structural Transformations Giving B-equivalent PT-Nets. In: Pagnoni, A, Rozenberg, G. (ed.): Informatik-Fachberichte No. 66: Application and Theory of Petri Nets. pp14–28, Springer-Verlag (1983).
Best, E., Fernandez, C.: Notations and Terminology on Petri Net Theory. Second edition. Arbeitspapiere der GMD No. 195 (1987).
Best, E., Desel, J.: Partial Order Behaviour and Structure of Petri Nets. Arbeitspapiere der GMD No. 373 (1989). Accepted for publication in Formal Aspects of Computing.
Berthelot, G.: Transformations and Decompositions of Nets. LNCS 254: Petri Nets, Central Models and Their Properties, pp. 359–376 (1987).
Datta, A., Ghosh, S.: Synthesis of a Class of Deadlock-Free Petri Nets. Journal of the ACM, Vol. 31, No. 3, pp.486–506 (1984).
Desel, J.: Live and Safe Free-choice Systems without Frozen Token are Well-behaved Bipolar Synchronization Schemes. Forthcoming paper (1990).
Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked Directed Graphs. Journal of Computer and System Science 5, pp. 511–523 (1971).
Esparza, J; Silva, M.: Top-Down Synthesis of Live and Bounded Free Choice Nets. 11th International Conference on Application and Theory of Petri Nets, Paris (1990).
Genrich, H.J., Thiagarajan, P.S.: A Theory of Bipolar Synchronization Schemes. TCS Vol. 30, pp.241–318 (1984).
Hack, M.: Analysis of Production Schemata by Petri Nets. TR-94, MIT-MAC (1972).
Suzuki, I.; Murata, T.: A Method for Stepwise Refinement and Abstraction of Petri Nets. Journal of Computer and System Sciences, Vol. 27, pp. 51–76 (1983).
Thiagarajan, P.S.: Elementary Net Systems. In: Brauer, W., Reisig, W., Rozenberg, G. (ed): LNCS 254: Petri Nets, Central Models and Their Properties, pp. 26–59 (1987).
Valette, R.: Analysis of Petri Nets by Stepwise Refinements. Journal of Computer and System Sciences, Vol. 18, pp. 35–46 (1979).
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Desel, J. (1990). Reduction and design of well-behaved concurrent systems. In: Baeten, J.C.M., Klop, J.W. (eds) CONCUR '90 Theories of Concurrency: Unification and Extension. CONCUR 1990. Lecture Notes in Computer Science, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039059
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DOI: https://doi.org/10.1007/BFb0039059
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