Introduction

Abstract

The fundamental results of Büchi [Büc62] and Rabin [Rab69] state that the monadic second-order (mso) theory of the $\omega$-chain $(\omega ,\leqslant )$ and of the complete binary tree $\big (\{0,1\}^*, {\preceq }, {\leqslant _{\mathrm {lex}}}\big )$ is decidable. In both cases the proof relies on a class of finite automata with expressive power equivalent to mso. Because of effective closure properties and decidability of the emptiness problem, the languages of $\omega$-words and infinite trees definable in mso are called regular. For a broad introduction to the field of regular languages of infinite objects see [Tho96, PP04, TL93].