© 2016

Descriptive Set Theoretic Methods in Automata Theory

Decidability and Topological Complexity


Part of the Lecture Notes in Computer Science book series (LNCS, volume 9802)

Also part of the Theoretical Computer Science and General Issues book sub series (LNTCS, volume 9802)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Michał Skrzypczak
    Pages 1-26
  3. Subclasses of Regular Languages

    1. Front Matter
      Pages 27-27
    2. Michał Skrzypczak
      Pages 29-36
    3. Michał Skrzypczak
      Pages 37-43
    4. Michał Skrzypczak
      Pages 45-69
    5. Michał Skrzypczak
      Pages 71-89
  4. Thin Algebras

    1. Front Matter
      Pages 91-91
    2. Michał Skrzypczak
      Pages 93-119
    3. Michał Skrzypczak
      Pages 121-135
    4. Michał Skrzypczak
      Pages 137-156
  5. Extensions of Regular Languages

    1. Front Matter
      Pages 157-157
    2. Michał Skrzypczak
      Pages 159-171
    3. Michał Skrzypczak
      Pages 173-181
    4. Michał Skrzypczak
      Pages 205-206
  6. Back Matter
    Pages 207-211

About this book


The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections between advanced concepts in logic, descriptive set theory, topology, and automata theory and provides many deep insights into the interplay between these fields. It opens new perspectives on central problems in the theory of automata on infinite words and trees and offers very impressive advances in this theory from the point of view of topology.

"…the thesis of Michał Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas.” Thomas Colcombet.


automata decidability descriptive complexity regular languages topological methods

Authors and affiliations

  1. 1.University of Warsaw WarsawPoland

About the authors

Michał Skrzypczak completed a double degree master program in Mathematics and Computer Science at University of Warsaw. His PhD thesis, defended in December 2014, was jointly supervised by Prof. Mikołaj Bojańczyk (Warsaw) and Prof. Igor Walukiewicz (Bordeaux). During the academic year 2014/2015 he was a PostDoc at IRIF in Paris, under supervision of Prof. Thomas Colcombet. Currently, Michał Skrzypczak is an assistant Professor at University of Warsaw.

Bibliographic information

Industry Sectors
IT & Software


“The author applies, with considerable success, a breadth of methods covering descriptive set theory, automata theory, logic and even some classical set theory, to questions on ω- and tree automata. ... he has managed to present basic material and his own results in such a way as to make these developments accessible to the reader. ... should be useful for those who wish to keep in touch with recent developments in automata theory.” (Roger Villemaire, zbMATH 1375.03003, 2018)

“The book shows how various techniques from descriptive set theory and logic can be effectively used in the study and understanding of automata theory. The interplay between topological and automata-theoretic methods is presented very nicely and should be useful to researchers in this area.” (Rana Barua, Mathematical Reviews, September, 2017)