{\omega}-Automata

TL;DR

This paper provides a comprehensive overview of {}-automata, covering types, operations, constructions, algebraic properties, and applications, serving as an introductory resource for automata theory related to infinite words.

Contribution

It offers a concise, structured introduction to {}-automata, including fundamental constructions and algebraic aspects, suitable as a foundational chapter in automata theory literature.

Findings

Detailed descriptions of automata types and modes

Automata constructions for boolean operations and determinization

Connections to algebraic structures and logic applications

Abstract

This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating automata), and directions (forward or backward automata). The main focus is on fundamental automata constructions, for instance, for boolean operations, determinization, disambiguation, and removing alternation. It also covers some algebraic aspects such as congruences for {\omega}-automata (and {\omega}-languages), basic structure theory (loops), and applications in mathematical logic. This paper may eventually become a chapter in a handbook of automata theory.