Control of ω-automata under state fairness assumptions

Abstract

This article studies the deadlock-free control of finite automata subject to specifications in the form of Rabin acceptance conditions. Automata are assumed to satisfy a state fairness condition, whereby any transition that is infinitely often enabled (by both the underlying dynamics and the control mechanism) must eventually occur. The problem of computing the automaton’s controllability subset – the set of states from which it can be controlled to satisfy its acceptance condition – is solved through a fixpoint characterization of this state subset. The state fairness condition simplifies the fixpoint characterization and allows the controllability subset to be computed in polynomial time. The problem represents a modified version of Church’s problem and the emptiness problem for automata on infinite trees, and has potential applications to the verification and synthesis of reactive systems and to supervisory control.