Logic, Computation, Hierarchies

Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists. Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.

Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger.

Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures. Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Bochi, McNaughton and Schätzenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures Preface; Contents; The life and work of Victor L. Selivanov; Tight extensions of T0-quasi-metric spaces; On the strongly bounded turing degrees of simple sets; Levels of discontinuity, limit-computability, and jump operators; The wadge hierarchy of Petri Nets?-languages; Diophantine properties of brownian motion: recursive aspects; The completeness of isomorphism; Complexity issues for Preorders on finite labeled forests; Boolean algebras of regular quasi-aperiodic languages; A simple indeterminate infinite game In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by leading researchers in mathematical logic. Published in honor of Victor L Selivanov, this book collects 17 articles that inform on the developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This first chapter constitutes an introduction to the theory of automata on infinite words.