In: 96: Hildesheimer Informatik-Berichte 4. 1996. Computing Center, Novosibirsk, Russia; www.iis.nsk.su/persons/itar/.
Abstract: The paper is devoted to the investigation of equivalence notions used to abstract from concrete behavioural aspects of concurrent systems which are modelled by Petri nets. The basic behavioural equivalences known from the literature are supplemented by new ones to obtain the complete picture and examined for all class of nets as well as for some of their subclasses: sequential nets (nets without concurrency) and strictly labelled nets (which are isomorphic to nonlabelled nets). For top-down design of concurrent systems refinement is used which is the inverse operator to abstraction of concrete structure of such systems. An important property of equivalence notions is their preservation by refinements which guarantees equivalence of systems to be modelled on different levels of abstraction. All of considered equivalence notions are checked for preservation by refinements.
Keywords: Petri nets; sequential nets; strictly labelled nets; behavioural equivalences; bisimulation; refinement.