# Finite Automata and the Infinite

**Professor Wolfgang Thomas**

**RWTH Aachen University, Germany**

**Abstract:**

Finite automata are a simple model of computation, yet they offer intriguing difficulties – and results – when used in the description and analysis of infinite objects. These objects may arise as infinite-state systems, infinite computations (such as computation trees), or a combination of both. Automata serve here as a tool to make logic over infinite structures effective, which in turn has led to many applications in algorithmic verification and synthesis. The lecture offers a personal account of the development of automata theory with this focus. Starting from a historical discussion, we give an intuitive explanation of central results (regarding automata over infinite strings and trees, and infinite games), and then address some open problems on the interplay between automata theory and logic.

The lecture will be followed by a informal reception.

**Biography:**

Wolfgang Thomas obtained the degree of M.Sc. (1972) from the University of Bristol and the doctoral degree (1975) from the University of Freiburg, Germany, both in mathematical logic. He was professor for computer science at RWTH Aachen University 1982-1989, at the University of Kiel 1989-1998, and since 1998 again in Aachen on the chair “Logic and Theory of Discrete Systems”. He co-authored a monograph on mathematical logic and is known for numerous contributions to automata theory and logic, among them influential survey papers. He served in many PCs (chairing, e.g., FoSSaCS, STACS, ICALP) and as editor of journals, among them ACM Transactions of Computational Logic and Logical Methods in Computer Science. He is doctor honoris causa of the Ecole Nomale Supérieure de Cachan and the University of Mons, member of Academia Europaea, and Fellow of EATCS (European Association of Computer Science).

**Short Course: Finite Automata and the
Infinite - a Technical Survey**

**Professor Wolfgang Thomas**

**RWTH Aachen University, Germany**

Finite automata over infinite strings and trees have opened a new chapter of effective model theory, mostly in connection with monadic second-order logic (MSO-logic). The classical results of the 1960’s, by Büchi, McNaughton, Rabin, and others have been a subject of intensive study over several decades, giving (1) refined and streamlined presentations, (2) extensions especially on MSO-logic over infinite transition systems, and (3) an adaption of the fundamental results towards practical use.

We survey the state of the art with a focus on the first two aspects, proceeding in four stages:

• Büchi automata and their determinization

• Regular infinite games

• Rabin’s tree theorem

• Muchnik’s theorem, unfolding, and the pushdown hierarchy

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