Formulation of Cell Petri Nets

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Abstract

Based on the Petri net definitions and theorems already formalized in the Mizar article [13], in this article we were able to formalize the definition of cell Petri nets. It is based on [12]. Colored Petri net has already been defined in [11]. In addition, the conditions of the firing rule and the colored set to this definition, that defines the cell Petri nets are further extended to CPNT.i further. The synthesis of two Petri nets was introduced in [11] and in this work the definition is extended to produce the synthesis of a family of colored Petri nets. Specifically, the extension to a CPNT family is performed by specifying how to link the outbound transitions of each colored Petri net to the place elements of other nets to form a neighborhood relationship. Finally, the activation of colored Petri nets was formalized.

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  • [1] Grzegorz Bancerek. K¨onig’s theorem. Formalized Mathematics 1(3):589-593 1990.

  • [2] Grzegorz Bancerek. Free term algebras. Formalized Mathematics 20(3):239-256 2012. doi:10.2478/v10037-012-0029-6.

  • [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics 1(1):41-46 1990.

  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics 1(1):91-96 1990.

  • [5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics 1(1): 55-65 1990.

  • [6] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics 1(1):153-164 1990.

  • [7] Czesław Bylinski. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics 1(3):521-527 1990.

  • [8] Czesław Bylinski. Partial functions. Formalized Mathematics 1(2):357-367 1990.

  • [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics 1(1):47-53 1990.

  • [10] Agata Darmochwał. Finite sets. Formalized Mathematics 1(1):165-167 1990.

  • [11] Mitsuru Jitsukawa Pauline N. Kawamoto Yasunari Shidama and Yatsuka Nakamura. Cell Petri net concepts. Formalized Mathematics 17(1):37-42 2009. doi:10.2478/v10037-009-0004-z.

  • [12] Pauline N. Kawamoto and Yatsuka Nakamura. On Cell Petri Nets. Journal of Applied Functional Analysis 1996.

  • [13] Pauline N. Kawamoto Yasushi Fuwa and Yatsuka Nakamura. Basic Petri net concepts. Formalized Mathematics 3(2):183-187 1992.

  • [14] Krzysztof Retel. Properties of first and second order cutting of binary relations. Formalized Mathematics 13(3):361-365 2005.

  • [15] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics 1(1): 115-122 1990.

  • [16] Andrzej Trybulec. Many sorted sets. Formalized Mathematics 4(1):15-22 1993.

  • [17] Michał J. Trybulec. Integers. Formalized Mathematics 1(3):501-505 1990.

  • [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics 1(1):67-71 1990.

  • [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics 1 (1):73-83 1990.

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