Input-driven automata on well-nested infinite strings: automata-theoretic and topological properties

TL;DR

This paper studies input-driven automata on well-nested infinite strings, providing a complete characterization of their languages, determinization results, and insights into their topological complexity.

Contribution

It offers a novel characterization of automata on well-nested infinite strings, linking them to classical omega-regular languages and establishing determinization and Wadge degree results.

Findings

Complete characterization of omega-languages for well-nested input-driven automata

Determinization results for these automata

First analysis of their Wadge degrees

Abstract

Automata operating on strings of nested brackets, known as input-driven pushdown automata, and as visibly pushdown automata, have been studied since the 1980s. They were extended to the case of infinite strings by Alur and Madhusudan ("Visibly pushdown languages", STOC 2004). This paper investigates the properties of these automata under the assumption that a given infinite string is always well-nested. This restriction enables a complete characterization of the corresponding $\omega$-languages in terms of classical $\omega$-regular languages and input-driven automata on finite strings. This characterization leads to a determinization result for these automata, as well as to the first results on their Wadge degrees.