Descriptive Set Theoretic Methods in Automata Theory: Decidability and Topological Complexity

by Michal Skrzypczak

Overview

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.

Product Details

ISBN-13:	9783662529461
Publisher:	Springer Berlin Heidelberg
Publication date:	08/06/2016
Series:	Lecture Notes in Computer Science , #9802
Edition description:	1st ed. 2016
Pages:	211
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

Subclasses of regular languages.- Thin algebras.- Extensions of regular languages.

Editorial Reviews

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)

From the Publisher