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W. Korczynski (1997)
ON A MODEL OF CONCURRENT SYSTEMSDemonstratio Mathematica, 30
(1996)
o r c z y n s k i , On a notion of Petri net morphisms
(1997)
G o l a n , A framework for consideration of fuzzy Petri nets
(1999)
G o l a n
(1998)
A framework for Dynamic Modelling of Information Systems; Petri Nets on Difference-ordered Hemirings
(1992)
G o l a n , The Theory of Semirings, with Applications in Mathematics and Theoretical Computer
(1994)
o r c z y n s k i
DEMONSTRATIO MATHEMATICAVol. XXXIIINo 12000Jonathan S. GolanSEMIRING-VALUED KORCZYNSKI NETSAbstract. Korczynski [4]-[6] generalized the notion of a Petri net by introducing thenotion of an e-net. The purpose of this generalization, based on a nonstandard definitionof a directed graph, was to allow a wider class of morphisms, including those which sendedges to vertices. Around the same time, Golan [2] introduced the notion of a semiringvalued Petri net in order to present a common framework which includes classical Petrinets, colored Petri nets, fuzzy Petri nets, etc. In this note we use the same techniques forpresenting semiring-valued Korczynski nets, which contain semiring-valued Petri nets asa special case.1. Notation and terminologyFor nonempty sets X and Y, we will denote the set of all functions fromX to Y by Y x . Functions inare always written as acting on the left.Any function a:X —* X can be extended to a function Ya:Yx—> Y xby setting Ya:g >-> ga. Note that if a,/3:X -* X then YaY? = Y0a. AY-valued relation on X is an element of YXxX.There is a bijective correspondence between the family of all subsets of aset X and B*, where B = {0,1}, through which a subset A of X correspondsto its characteristic
Demonstratio Mathematica – de Gruyter
Published: Jan 1, 2000
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