Abstract
The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets. When the synthesis problem has a solution, the set of regions viewed as properties of states provides a set-theoretic representation of the transition system. We show that such correspondences between nets and transition systems can be described as dualities induced by schizophrenic objects, leading further the analogy with classical representation theorems and giving us a means to describe uniformly previously known translations between nets and automata.
This work was partly supported by the project Mask of the E.C. program Science.
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References
Arnold, A., and Nivat, M., Comportements de processus. Colloque AFCET « Les Mathématiques de l'Informatique », (1982) 35–68.
Badouel, E., and Darondeau, Ph., Trace Nets. REX workshop, Beekbergen “Semantics: Foundation and Applications”, Springer-Verlag Lecture Notes in Computer Science, vol. 666 (1993) 21–50.
Bernardinello, L., De Michelis, G., and Petruni, K., Synchronic distances as Generalized Regions. Rapporto Interno n. 107-93, Dipartimento di Scienze dell'Informazione, Universitá degli Studi di Milano (1993).
Droste, M., and Shortt, R.M., Petri Nets and Automata with Concurrency Relations — an Adjunction, in ”Semantics of Programming Languages and Model Theory”, M. Droste and Y. Gurevich eds(1993) 69–87.
Ehrenfeucht, A., and Rozenberg, G., Partial 2-structures; Part I: Basic Notions and the Representation Problem, and Part II: State Spaces of Concurrent Systems, Acta Informatica, vol 27 (1990).
Isbell, J. R., General Functorial Semantics, I., American Journal of Mathematics, vol 94 (1972) 535–596.
Johnstone, P.T., Stone Spaces. Cambridge University Press, (1982).
Mukund, M., Petri Nets and Step Transition Systems. International Journal of Foundation of Computer Science, vol 3, nℴ 3 (1993).
Porst, H.-E., and Tholen, W., Concrete Dualities. In “Category Theory at Work”, H. Herrlich, and H.-E. Porst (eds.), Heldermann Verlag Berlin (1991) 111–136.
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Badouel, E., Darondeau, P. (1995). Dualities between nets and automata induced by schizophrenic objects. In: Pitt, D., Rydeheard, D.E., Johnstone, P. (eds) Category Theory and Computer Science. CTCS 1995. Lecture Notes in Computer Science, vol 953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60164-3_18
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DOI: https://doi.org/10.1007/3-540-60164-3_18
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