Integrating Temporal Logic as a State-Based Specification Language for Discrete-Event Control Design in Finite Automata

Abstract

This paper presents and analyzes a correct and complete translation algorithm that converts a class of propositional linear-time temporal-logic (PTL) formulae to deterministic finite (-trace) automata. The translation algorithm is proposed as a specification interface for finitary control design of discrete-event systems (DESs). While there has been a lot of computer science research that connects PTL formulae to omega-automata, there is relatively little prior work that translates state-based PTL formulae in the context of a finite-state DES model, to event-based finite automata-the formalism on which well-established control synthesis methods exist. The proposed translation allows control requirements to be more easily described and understood in temporal logic, widely recognized as a useful specification language for its intuitively appealing operators that provide the natural-language expressiveness and readability needed to express and explain these requirements. Adding such a translation interface could therefore effectively combine specifiability and readability in temporal logic with prescriptiveness and computability in finite automata. The former temporal-logic features support specification while the latter automata features support the prescription of DES dynamics and algorithmic computations. A practical implementation of the interface has been developed, providing an enabling technology for writing readable control specifications in PTL that it translates for discrete-event control synthesis in deterministic finite automata. Two application examples illustrate the use of the proposed temporal-logic interface. Practical implications of the complexity of the translation algorithm are discussed.