Abstract
In this paper, we supplement the set of basic and back-forth behavioural equivalences for Petri nets considered in [11] by place bisimulation ones. The relationships of all the equivalence notions are examined, and their preservation by refinements is investigated to find out which of these relations may be used in top-down design. It is demonstrated that the place bisimulation equivalences may be used for the compositional and history preserving reduction of Petri nets. In addition, we consider all the mentioned equivalences on sequential nets which are a special subclass of general Petri nets modelling sequential systems, where no two actions can happen simultaneously. On this net subclass all pomset equivalences merge with the corresponding interleaving ones, and it allows us to simplify their check.
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