Computability and Randomness

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

This book is open access under a CC BY 4.0 license.This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with e

In a textbook on probability and random numbers for students who have completed first-year university calculus, Sugita presents well-known basic theorems with proofs that are not seen in usual prob

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individ

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics an

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas

Describes the quests of two great physicists who both balked at the randomness of quantum mechanics and sought to explain it, at first as collaborators but then as competitors.

In the 1930s a series of seminal works published by Alan Turing, Kurt Godel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizatio

Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand

This book involves the design and analysis of coordination algorithms on networks, identification of dynamic networks, and estimation on networks with random geometries with implications for networks

In this second volume of The Sparks of Randomness, Henri Atlan pursues his investigation of human life, which he grounds in a distinctive intermingling of the biological and cognitive sciences and tra

This volume provides an account of the current state of the theory of combinatory spaces and discusses various applications. Here the term `combinatory space' can be regarded as a system for functi

Tice pursues aspects of statistical physics that relate to telecommunications and the study of natural languages. Here he addresses the notion of compression ratios greater than have been known for ra

Computability Theory: An Introduction to Recursion Theory, provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic c

The Sparks of Randomness, Henri Atlan's magnum opus, develops his whole philosophy with a highly impressive display of knowledge, wisdom, depth, rigor, and intellectual and moral vigor. Atlan founds a

The Sparks of Randomness, Henri Atlan's magnum opus, develops his whole philosophy with a highly impressive display of knowledge, wisdom, depth, rigor, and intellectual and moral vigor. Atlan founds a

Proper treatment of structural behavior under severe loading - such as the performance of a high-rise building during an earthquake - relies heavily on the use of probability-based analysis and decisi

Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the moder

Combining classic theory with unique applications, this crisp narrative is supported by abundant examples and clarifies key concepts by introducing important uses of techniques in real systems. Broad-