Maximally permissive controlled system synthesis for non-determinism and modal logic

Abstract

We propose a new technique for controlled system synthesis on non-deterministic automata for requirements in modal logic. Synthesis, as defined in this paper, restricts a behavioral specification of the uncontrolled system such that it satisfies a given logical expression, while adhering to the rules dictated by supervisory control such as maximal permissiveness and controllability. The applied requirement formalism extends HennessyMilner logic with the invariant and reachability modalities from Gödel-Löb logic, and is therefore able to express a broad range of control requirements, such as marker state reachability and deadlock-freeness. This paper contributes to the field of control synthesis by achieving maximal permissiveness in a non-deterministic context for control requirements in modal logic, and treatment of controllability via partial bisimulation. We present a well-defined and complete derivation of the synthesis result, which is supported further by computer-verified proofs created using the Coq proof assistant. The synthesis method is also presented in algorithmic form, including an analysis of its computational complexity. We show that the proposed synthesis theory allows full expressibility of Ramadge-Wonham supervisory control theory and we illustrate its applicability in two small industrial case studies, including an analysis with regard to scalability.

Comparing Controlled System Synthesis and Suppression Enforcement

“…Identifying such a technique enables the possibility of adopting a multi-pronged enforcement approach. One possible candidate is controlled system synthesis (CSS) [24,9,14,30]: it analyses the state space of the SuS and reformulates it pre-deployment by removing the system's ability to execute erroneous behaviour. As a result, a restricted (yet valid) version of the SuS is produced; this is known as a controlled system.…”

“…In this first attempt, we however limit ourselves to study this relationship in the context of safety properties. As a vehicle for this comparison, we choose the recent work on CSS by van Hulst et al [24], and compare it to our previous work, presented in [5], on enforcing safety properties via action suppressions. We chose these two bodies of work as they are accurate representations of the two techniques.…”

“…To further simplify our comparison, we formulate both techniques in a core common setting and show that there are subtle differences between them even in that scenario. Specifically, we identify a common core within the work presented in [5,24] by:…”

“…working with respect to the Safe Hennessy Milner Logic with invariance (sHML inv ), that is, the intersection of the logics used by both works, namely, the Safe Hennessy Milner Logic with recursion (sHML) in [5] and the Hennessy Milner Logic with invariance and reachability (HML reach inv ) in [24], removing constructs and aspects that are supported by one technique and not by the other, and by taking into account the assumptions considered in both bodies of work.…”

“…Section 2 provides the necessary preliminary material describing how we model systems as labelled transition systems and properties via the chosen logic. In Section 3 we give an overview of the equalized and simplified versions of the enforcement model presented in [5] and the controlled system synthesis rules of [24]. Section 4 then compares the differences and similarities between the two models, followed by our first contribution which disproves the observational equivalence of the two techniques.…”