Descriptive Set Theoretic Methods in Automata Theory

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 Micha Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas. Thomas Colcombet.

This thesis is devoted to studying problems of automata theory from the point of view of descriptive set theory Providing effective characterisations of regular languages of infinite trees For game automata, for languages of thin trees Includes supplementary material: sn.pub/extras

Autorentext

Michä 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. Miko aj Bojäczyk (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, Michä Skrzypczak is an assistant Professor at University of Warsaw.

Klappentext

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 Michä Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas. Thomas Colcombet.

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