Compositional synthesis and most general controllers

Given a formal model of the behavior of a system, an objective and some notion of control the goal of controller synthesis [RW87, Won89] is to construct a (finite-state) controller that ensures that the system always satisfies the objective. Often, the controller can base its decisions only on limited observations of the system. This notion of limited observability induces a partial-information game between the controller and the uncontrollable part of the system. A successful controller then realizes an observation-based strategy that enforces the objective. In this thesis we consider the controller synthesis problem in the linear-time setting where the behavior of the system is given as a nondeterministic, labeled transitions system A, where the controller can only partially observe and control the behavior of A. The goal of the thesis is to develop a compositional approach for constructing controllers, suitable to treat conjunctive cascades of linear-time objectives Φ1,Φ2, . . . ,Φk in an online manner. We iteratively construct a controller C1 for system A enforcing Φ1, then a controller C2 enforcing Φ2 for the parallel composition of the first controller with the system, i.e., C1 ./ A, and so on. It is crucial for this approach that each controller Ci enforces Φi in a most general manner, being as permissive as possible. Otherwise, behavior that is needed to enforce subsequent objectives could be prematurely removed. Standard notions of strategies and controllers only allow the most general treatment for the limited class of safety objectives. We introduce a novel concept of most general strategies and controllers suited for the compositional treatment of objectives beyond safety. We demonstrate the existence of most general controllers for all enforceable, observation-based ω-regular objectives and provide algorithms for the construction of such most general controllers, with specialized variants for the subclass of safety and co-safety objectives. We furthermore adapt and apply our general framework for the compositional synthesis of most general controllers to the setting of exogenous coordination in the context of the channel-based coordination language Reo [Arb04] and the constraint automata framework [BSAR06] and report on our implementation in the verification toolset Vereofy. The construction of most general controllers in Vereofy for ω-regular objectives relies on our tool ltl2dstar for generating deterministic ω-automata from Linear Temporal Logic (LTL) formulas. We introduce a generic improvement for exploiting insensitiveness to stuttering during the determinization construction and evaluate its effectiveness in practice. We further investigate the performance of recently proposed variants of Safra’s determinization construction in practice.