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Formulation of Cell Petri Nets

100%
Jitsukawa M., Kawamoto P. N., Shidama Y.
Formalized Mathematics
|
2013
|
tom 21
|
nr 4
241-247
EN
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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Detection of deadlocks and traps in Petri nets by means of Thelen's prime implicant method

70%
Węgrzyn A., Karatkevich A., Bieganowski J.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 1
113-121
EN
A new method of detecting deadlocks and traps in Petri nets is presented. Deadlocks and traps in Petri nets can be represented by the roots of special equations in CNF form. Such equations can be solved by using the search tree algorithm proposed by Thelen. In order to decrease the tree size and to accelerate the computations, some heuristics for Thelen's method are presented.
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