Emptiness Problem For Automata Research Articles

Control of ω-automata under state fairness assumptions

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.

Control of Infinite Behavior of Finite Automata

A problem in the control of automata on infinite strings is defined and analyzed. The key to the investigation is the development of a fixpoint characterization of the of a deterministic Rabin automaton, the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The fixpoint representation allows straightforward computation of the controllability subset and the construction of a suitable state-feedback control for the automaton. The results have applications to control synthesis, automaton synthesis, and decision procedures for logical satisfiability; in particular, they represent a direct, efficient and natural solution to Church's problem, the construction of winning strategies for two-player zero-sum $\omega$-regular games of perfect information, and the emptiness problem for automata on infinite trees.