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 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.

Słowa kluczowe: automata, infinite trees, topological methods, automaty, drzewa nieskończone, metody topologiczne.

The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed proceedings of the 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised full papers presented were carefully reviewed and selected from 507 submissions. The papers are organized in the following three tracks: algorithms, complexity, and games; logic, semantics, automata and theory of programming; and foundations of networked computation: models, algorithms and information management.

This book constitutes the proceedings of the 20th International Conference on Developments in Language Theory, DLT 2016, held in Montreal, QC, Canada, in July 2016. The 32 full papers and 4 abstracts of invited papers presented were carefully reviewed and selected from 48 submissions. This volume presents current developments in formal languages and automata, especially from the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphs, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis; polyominoes and bidimentional patterns; cryptography; concurrency; cellular automata; bio-inspried computing; quantum computing.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Most previous research relies on transformations of programs in order to reduce a verification problem to problems that can be solved using classical techniques such a refinement mappings and well-founded orderings. Progress measures, the key innovation of this thesis, provide direct, syntax-independent verification techniques for a wide range of specifications.

1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ... , 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.

The purpose of this volume is to bring together a number of elements that would be useful in the construction of a coherent and comprehensive theory of biology. Based on the assumption that living systems represent some kind of "organized complexity," the collection discusses meaningful ways of formulating two basic questions: what is the nature of this complexity; and, what are the principles of its organization? The question always asked about biological theory is whether or not it constitutes useful scientific theory. Because many useful biological theories cannot yet be made explicit in terms of conventional physics, Sketching Theoretical Biology illustrates the types of questions in biology that correspond to the types of issues discussed in theoretical physics. This book, originally published in 1969, centers around a vigorous debate on the role played by metaphysical beliefs in determining scientific attitudes. The discussion covers heredity and evolution, cognitive processes and control processes, general property of hierarchies, and the current status of neo-Darwinism. Contributors include theoretical physicists, philosophers, neuroscientists, theoretical chemists, computer scientists, chemical engineers, geneticists and molecular biologists.