Rule-Based Refinement of Petri Nets: A Survey

Abstract

Abstract. This contribution provides a thorough survey of our work on rule-based refinement. Rule-based refinement comprises the transformation of Petri nets using rules while preserving certain system properties. Petri net rules and transformations are expressed by morphisms and pushouts. This allows an abstract formulation of our notions independent of a specific Petri net class, as place/transition nets, elementary nets, predicate/transition nets etc. Hence, it is adequate to consider our approach as rule-based refinement of Petri nets in general. We have presented various results in recent years at different conferences. So this contribution gives an overview of our work in a compact form leaving out the technical details.

Invariant preservation in iterative modeling

“…Our future research is concerned with an extension to enhance our theory to preserve other kinds of properties besides invariants, for example liveness properties [10], temporal properties, etc by using existing work in the literature. Furthermore, we would like to support the integration of modeling language with higher level of abstraction than Apn, namely Domain-Specific Languages in general.…”

“…Our contribution extends Padberg's result published in [19,20] but as already mentioned, this result does not consider guard strengthening. To the best of our knowledge, Padberg's work on this topic has been discontinued after a last survey paper [10] has been published on the topic in 2003.…”

Petri Net Transformations

“…For place/transition nets, algebraic high-level nets and Coloured Petri nets the most important results for rule-based refinement are presented in Table 1. For more details see [27]. Table 1.…”

An approach for specification construction using property-preserving refinement patterns

“…There are some research results on rule-based refinement of high-level nets [11,12]. Seldom research focus on refinements of PrT nets.…”