Finite - state Automata on In nite Inputs

This paper is a self-contained introduction to the theory of nite-state automata on innnite words. The study of automata on innnite inputs was initiated by B uchi in order to settle certain decision problems arising in logic. Subsequently, there has been a lot of fundamental work in this area, resulting in a rich and elegant mathematical theory. In recent years, there has been renewed interest in these automata because of the fundamental role they play in the automatic veriication of nite-state systems.