Stepwise Introduction and Preservation of Safety Properties in Algebraic High-Level Net Systems

Abstract

Our approach of rule-based refinement 1 provides a formal description for the stepwise system development based on Petri nets. Rules with a left-hand and a right-hand side allow replacing subnets in a given algebraic high-level net system. The extension of these rules supports the preservation of system properties. In this paper we extend the preservation of safety properties significantly. We define rules, that introduce new safety properties. In our new approach we propose first the verification of properties at the moment they can be expressed and then their preservation further on. Hence, properties can be checked as long as the system is still small. Moreover, introducing properties allows checking these for the relevant subpart only. Changes that are required later on can be treated the same way and hence preserve the system properties. Hence, we have made a step towards a formal technique for the stepwise system development during analysis and design.

Rule-Based Refinement of Petri Nets: A Survey

“…This approach is in line with previous publications concerning rule-based modification preserving safety properties of nets, see e.g. [13,15,14]. A related idea has been pursued in [DA92], where various reduction methods for ordinary nets have been proposed.…”

“…Theorem [15,11]. Given a rule (r = (L ← K → R), f : L → R) with f being -either a place preserving morphism -or a transition gluing morphism then for a transformation step N 1 (r,f ) =⇒ N 2 holds:…”

“…Theorem [15,11]. Given a rule (r, f ) with r = (∅ ← ∅ → R) so that R |= ϕ with a occurrence g : R → N 2 .…”

“…Subsequently we refer to conference papers [15,11,16], but due to space limitations there many proofs are given in more detail in the corresponding technical reports [6,12,8].…”

An approach for specification construction using property-preserving refinement patterns

“…Also the author presented a list of formal transformations (re-writing rules) for PrT nets that are consistent with equivalence. In [10], they introduce place preserving morphism and transition gluing morphism, which preserve safety property. They show the refinement steps through an example, which is based on a high-level Petri nets.…”