Conflicts and Projections

Abstract

This paper studies abstraction methods suitable to verify very large models of discrete-event systems to be nonconflicting. It compares the observer property to methods known from process algebra, namely to conflict equivalence and observation equivalence. The observer property is shown to be the property that corresponds to conflict equivalence in the case where natural projection is used for abstraction. In this case, the observer property turns out to be the least restrictive condition that can be imposed on natural projection to enable compositional reasoning about conflicts. The observer property is also shown to be closely related to observation equivalence. Several examples and propositions are presented to relate different aspects of these methods of abstraction. Copyright 2007 IFAC

On the use of observation equivalence in synthesis abstraction

“…Blocking states can always be merged while ensuring synthesis abstraction, but this cannot be done via observation equivalence. For blocking automata, the relationship to projection is similar to the results in [18].…”

“…x ∈ Q such that P Ω (s) = P Ω (s ′ ), G stω −→, and G s ′ → x, there exists t ′ ∈ Σ * such that P Ω (t ′ ) = P Ω (t) and x t ′ ω →; [18] • locally control-consistent (LCC) for G, if for all s ∈ Σ * , all υ ∈ Ω∩Σ u , and all states x ∈ Q such that G s → x and P Ω (s)υ ∈ P Ω L(G), if there exists t ∈ Υ * such that x tυ → then there also exists u ∈ (Υ ∩ Σ u ) * such that x uυ →. [8] Natural projection is a language-theoretic operation, which can be applied to automata using the standard algorithms of subset construction and minimisation [19].…”

“…It is known that Nerode equivalence implies observation equivalence if the projection satisfies the observer property [18], [20]; in this case, the quotient G/≡ Ω is a candidate for abstraction of G. On the other hand, not every observation equivalence abstraction can be expressed using projection.…”

Verification of Nonconflict of Supervisors Using Abstractions

“…The work presented in this paper makes use of the "observer property", as will be explained later. The relations between this property and the concepts of observation equivalence and conflict equivalence are established in [17]. Reference [18] applies the hierarchical scheme to implement nonblocking control.…”

Hierarchical modelling of manufacturing systems using discrete event systems and the conflict preorder

“…As an alternative, projection-based abstractions [10,35,42] do not impose a master-slave relationship. While these methods are not as structured as HISC, it is known that a projection that satisfies the observer property [25,42,43] can serve as an abstraction of a subsystem and thus as its interface. With additional requirements such as output control consistency [10] or local control consistency [30,35], it is also possible to ensure maximal permissiveness of supervisors when using synthesis.…”