A Short Introduction to Infinite Automata

Infinite automata are of interest not only in the verification of systems with infinite state spaces, but also as a natural (and so far underdeveloped) framework for the study of formal languages. In this survey, we discuss some basic types of infinite automata, which are based on the so-called prefix-recognizable, synchronized rational, and rational transition graphs, respectively. We present characterizations of these transition graphs (due to Muller/Schupp and to Caucal and students), mention results on their power to recognize languages, and discuss the status of central algorithmic problems (like reachability of given states, or decidability of the first-order theory).

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