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SEMIRING-VALUED KORCZYŃSKI NETS

SEMIRING-VALUED KORCZYŃSKI NETS 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

SEMIRING-VALUED KORCZYŃSKI NETS

Demonstratio Mathematica , Volume 33 (1): 8 – Jan 1, 2000

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References (7)

Publisher
de Gruyter
Copyright
© by Jonathan S. Golan
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2000-0103
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Demonstratio Mathematicade Gruyter

Published: Jan 1, 2000

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