Descriptive Set Theoretic Methods in Automata Theory
Decidability and Topological Complexity
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Beschreibung
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.
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
Autor*in
Michał Skrzypczak
Themen in »Descriptive Set Theoretic Methods in Automata Theory«
automata decidability descriptive complexity regular languages topological methods algorithm analysis and problem complexity
Stimmen zu »Descriptive Set Theoretic Methods in Automata Theory«
“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)
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