Affiliation:
1. Sberbank Technology, the Department of Frontal Components, The Center of Integration and Exploitation Services, St. Petersburg, Russia
2. Laboratory of Modern Algebra and Applications, St. Petersburg State University and St. Petersburg, Department of Steklov Mathematical Institute, St. Petersburg, Russia
Abstract
The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial [Formula: see text], and any directed finite bipartite graph can be considered as a polynomial [Formula: see text], and vise verse. We also show that the multiplication in the semirings [Formula: see text], [Formula: see text] corresponds to an operation of the corresponding graphs. This operation is exactly the product of Petri nets in the sense of Winskel [G. Winskel and M. Nielsen, Models of concurrency, in Handbook of Logic in Computer Science, Vol. 4, eds. Abamsky, Gabbay and Maibaum (Oxford University Press, 1995), pp. 1–148]. As an application, we give an approach to dividing in the semirings [Formula: see text], [Formula: see text], and a criteria for parallalization of Petri nets. Finally, we endow the set of all bipartite graphs with the Zariski topology.
Funder
the Government of the Russian Federation
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory