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.
Highlights
In this paper we study the properties of the resource similarity and resource bisimulation in Petri nets with invisible transitions (where some transitions may be labelled with an invisible label ( ) that makes their rings unobservable for an external observer)
In this paper the behavior of Petri nets is investigated from the standpoint of bisimulation equivalence. e fundamental notion of bisimulation was introduced by R
Two markings of a Petri net are called bisimilar if the choice of each of them as an initial marking gives the same visible behavior of the net
Summary
In this paper the behavior of Petri nets is investigated from the standpoint of bisimulation equivalence. e fundamental notion of bisimulation was introduced by R. Place bisimulations in Petri nets with invisible transitions were studied by C. There are speci c nontrivial subclasses of Petri nets with invisible transitions, that have some nice properties w.r.t. place bisimulation. It is shown that resource bisimulations can be e ectively computed in some non-trivial subclasses of nets with invisible transitions. It is shown that in the class of -saturated nets the weak transfer property of resource -bisimulation can be e ectively checked. It is shown that for a general class of Petri net with invisible transitions it is possible to construct a sequence of so-called ( , )-equivalences, approximating the largest -bisimulation of resources. On the Approximation of the Resource Equivalences in Petri Nets with the Invisible Transitions the parameterized underapproximation of largest -bisimulation.
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