On the Approximation of the Resource Equivalences in Petri Nets with the Invisible Transitions
https://doi.org/10.18255/1818-1015-2020-2-234-253
Abstract
Two resources (submarkings) are called similar if in any marking any one of them can be replaced by another one without affecting the observable behavior of the net (regarding marking bisimulation). It is known that resource similarity is undecidable for general labelled Petri nets. In this paper we study the properties of the resource similarity and resource bisimulation (a subset of complete similarity relation closed under transition firing) in Petri nets with invisible transitions (where some transitions may be labelled with an invisible label (τ) that makes their firings unobservable for an external observer). It is shown that for a proper subclass (p-saturated nets) the resource bisimlation can be effectively checked. For a general class of Petri net with invisible transitions it is possible to construct a sequence of so-called (n, m)-equivalences approximating the largest τ-bisimulation of resources.
Supporting agencies: RFBR, project No 17-07-00823.
About the Author
Vladimir A. Bashkin
P. G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
associate professor, doctor of science
14 Sovetskaya, Yaroslavl 150003
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Review
For citations:
Bashkin V.A. On the Approximation of the Resource Equivalences in Petri Nets with the Invisible Transitions. Modeling and Analysis of Information Systems. 2020;27(2):234-253. https://doi.org/10.18255/1818-1015-2020-2-234-253
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