Abstract
In the paper we study “first consume then produce” and “first produce then consume” causality of transition firings in Petri nets over partial algebra. We show that both causalities may be described by simple algebraic operations on transition systems, namely the compatible and linear operation. Thus, weak semantics (weak marking graph) corresponding to the “first consume then produce” causality is constructed by compatible operation on related net. Strong semantics (strong marking graph), which corresponds to consumption and production in any order, i.e., to combination of both causalities, is given by intersection of compatible and linear image of the related net. Furthermore, it is shown that the classes of weak and strong marking graphs of all Petri nets over arbitrary partial groupoids are equivalent up to isolated markings. The same equivalence is shown for classes of weak and strong marking graphs of all Petri nets over partial groupoids embeddable into Abelian groups.
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References
L. Bernardinello and F. De Cindio. A Survey of Basic Models and Modular Net Classes. In Advances in Petri Nets 1992, LNCS 609, pp. 304–351, 1992.
P. Braun. Ein allgemeines Petri-netz. Master’s thesis, Univ. of Frankfurt, 1992.
J. Desel and W. Reisig. Place/Transition Petri Nets. In Lectures on Petri nets I: Basic Models, LNCS 1491, pp. 123–174, 1998.
R. Devillers. The Semantics of Capacities in P/T Nets. In Advances in Petri Nets 1989, LNCS 424, pp. 128–150, 1990.
M. Droste and R. M. Shrott. Petri Nets and Automata with Concurrency Relation—an Adjunction. In M. Droste and Y. Gurevich (eds) Semantics of Programming Languages and Model Theory, Gordon and Breach Sc. Publ., pp. 69–87, 1993.
M. Hack. Petri Nets and Commutative Semigroups. Computation Structures Note No. 18, Project MAC, M.I.T., July 1974.
H. J. Hoogeboom and G. Rozenberg. Diamond properties of elementary net systems. Fundamenta Informaticae, XIV:287–300, 1991.
G. Juhás. The essence of Petri nets and transition systems through Abelian groups. Electronic Notes in Theoretical Computer Science, 18, 1998.
G. Juhás. Reasoning about algebraic generalisation of Petri nets. In Proc. of 20 th International Conference on Theory and Application of Petri Nets, Williamsburg, VA, USA, Springer, LNCS 1639, pp. 324–343, 1999.
J. Meseguer and U. Montanari. Petri nets are monoids. Information and Computation, 88(2):105–155, October 1990.
J. Padberg. Abstract Petri Nets: Uniform Approach and Rule-Based Refinement. PhD thesis, Technical University of Berlin, 1996.
P. Tix. One FIFO place realizes zero-testing and Turing machines. Petri net Newsletter, 51, 12, 1996.
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Juhás, G. (1999). On Semantics of Petri Nets Over Partial Algebra. In: Pavelka, J., Tel, G., Bartošek, M. (eds) SOFSEM’99: Theory and Practice of Informatics. SOFSEM 1999. Lecture Notes in Computer Science, vol 1725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47849-3_29
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DOI: https://doi.org/10.1007/3-540-47849-3_29
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