Petri nets as bitopological spaces

• Autorzy: Korczyński W.
• Języki publikacji: EN

Abstrakty

EN

In the paper a topological presentation of Petri nets has been presented. The presentation is based on a closure operation defined for an arbitrary transitive and dense binary relation. Such relations lead to a natural definition of Petri nets as a special bitopological spaces. In the paper some elementare properties of such spaces-the counter parts of some properties of Petri nets-are described. The paper may be seen as a generalization of [3].

Słowa kluczowe

EN

operators; Petri nets; bitopological spaces

PL

ciągi Petriego; przestrzeń bitopologiczna; operatory

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 923--934
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Korczyński W.

• University of Art and Science, ul. Wesoła 52, 25-369 Kielce, Poland

Bibliografia

• [1] H. J. Genrich, K. Lautenbach, P. S. Thiagarajan, Elements of General Net Theory, in: W. Brauer (ed.) Net Theory and Applications, LNCS 84 Springer Verlag Berlin, Heidelberg, New York, 1080.
• [2] D. Hasse, M. Michler, Theorie der Kategorien, Akademie-Verlag, Berlin 1976.
• [3] J. C. Kelly, Bitopological spaces, Proc. London. Math. Soc. (3), 13 (1963), 71-89.
• [4] W. Korczyński, On a notion of Petri net morphisms, Arch. Inform. Teoret. Stos.Vol. 8 (3-4) (1996), 383-399.
• [5] W. Korczyński, On a topological prezentation of graphs, Demonstratio Math. 37 no 4 (2004), 761-771.
• [6] S. Mac Lane, Categories for the Working Mathematician, Springer Verlag, New York, 1971.
• [7] P. H. Starke, Analyse von Petri Netz Modellen, Teubner Verlag Stuttgart, 1990.
• [8] G. Winskel, A New Definition of Morphisms of Petri Nets, Proc. STACS'84, Springer LNCS 166, Springer Verlag, Berlin, Heidelberg, New York (1984).