Computability and Randomness

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The

This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability, i.e., algorithmic functions on certain countable structures in the ori

This textbook provides undergraduate students with an introduction to the basic theoretical models of computability, and develops some of the model's rich and varied structure. The first part of the b

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, wit

This book is concerned with the theory of computability and complexity over the real numbers. This theory was initiated by Turing, Grzegorczyk, Lacombe, Banach and Mazur and has seen rapid growth in

Analyzes Randomness in Major Genetic Processes and EventsNo matter how far science advances, the proportion of what is knowable to what is random will remain unchanged, and attempts to ignore this cri

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

Computability theory originated with the seminal work of Godel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and t

Together, Models and Computability and its sister volume Sets and Proofs will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, post-graduate researchers, and the informed and interested nonspecialist.

This textbook provides undergraduate students with an introduction to the basic theoretical models of computability, and develops some of the model's rich and varied structure. The first part of the b

Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general t

Language Computability and Formal Language Theory is a division of computer engineering, of mathematical reasoning, as well as one of the primary principles of computation. Language Computability and

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathemati

Includes access to student companion website.Updated to align to the latest 2013 ACM/IEEE Computer Science curricula, Discrete Structures, Logic, and Computability, Fourth Edition is designed for the

In this book the authors explain what computability means for data more complex than natural numbers and similar discrete data. In particular, they show how to develop a good theory of computability i

?This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ram

Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract

John Tyler Bonner, one of our most distinguished and insightful biologists, here challenges a central tenet of evolutionary biology. In this concise, elegantly written book, he makes the bold and prov

There are few notions as fundamental to contemporary science as those of computability and modelling. Computability and Models attempts to make some of the exciting and important new research developm

This review volume consists of an indispensable set of chapters written by leading scholars, scientists and researchers in the field of Randomness, including related subfields specially but not limite

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.

Everyone wants to succeed in life. But what causes some of us to be more successful than others? Is it really down to skill and strategy - or something altogether more unpredictable? This book is the

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are