Transition removal for compositional supervisor synthesis

Abstract

This paper investigates under which conditions transitions can be removed from an automaton while preserving important synthesis properties. The work is part of a framework for compositional synthesis of least restrictive controllable and nonblocking supervisors for modular discrete event systems. The method for transition removal complements previous results, which are largely focused on state merging. Issues concerning transition removal in synthesis are discussed, and redirection maps are introduced to enable a supervisor to process an event, even though the corresponding transition is no longer present in the model. Based on the results, different techniques are proposed to remove controllable and uncontrollable transitions, and an example shows the potential of the method for practical problems. I. INTRODUCTION Supervisory control theory [1] provides a general framework to compute least restrictive strategies to control a given plant such that its behaviour satisfies a given specification. Synthesis for systems with a large number of components is impeded by an inherent complexity problem known as state-space explosion. A lot of research has been devoted to overcome the state-space explosion problem, and also to find more comprehensible supervisors [1]-[3]. Compositional methods seek to avoid large state spaces using abstraction, and have been used in verification [4], [5] and synthesis [3], [6], [7]. In a system with a large number of components, it is often possible to simplify individual components before composing them with the rest of the system, achieving significant performance improvements. Several ways to simplify components have been investigated in recent years. Natural projection is a standard and effective way to compute abstractions, although strong restrictions need to be imposed to ensure the preservation of synthesis results [8], [9]. Observation equivalence [10] and conflict equivalence [11] are well-known abstraction methods for nonblocking verification [5], but for synthesis these abstractions can only be applied in combination with unobservable events [12], [13], which limits their applicability. Recently, frameworks for compositional synthesis based on abstractions of nondeterministic automata have been proposed [3], [6], [7], in some cases showing substantial reduction of the number of states encountered during synthesis. This paper seeks to enhance these methods by providing means to remove transitions. This is important, because for This work was supported by the Swedish Research Council.

Compositional synthesis of supervisors in the form of state machines and state maps

“…It is shown to be smaller than state machine-based supervisors [10], both by theoretic complexity analysis and by experiments. The new algorithm also performs better, because it permits nondeterminism, hiding, and transition removal [9], and avoids renaming.…”