Bücher der Reihe Theory and Applications of Computability

It is not always clear what computer programs mean in the various languages in which they can be written, yet a picture can be worth 1000 words, a diagram 1000 instructions.In this unique textbook/reference, programs are drawn as string diagrams in the language of categories, which display a universal syntax of mathematics (Computer scientists use them to analyze the program semantics; programmers to display the syntax of computations). Here, the string-diagrammatic depictions of computations are construed as programs in a single-instruction programming language. Such programs as diagrams show how functions are packed in boxes and tied by strings. Readers familiar with categories will learn about the foundations of computability; readers familiar with computability gain access to category theory. Additionally, readers familiar with both are offered many opportunities to improve the approach.Topics and features:Delivers a ¿crash¿ diagram-based course in theory of computationUses single-instruction diagrammatic programming languageOffers a practical introduction into categories and string diagrams as computational toolsReveals how computability is programmability, rather than an ¿ether¿ permeating computers Provides a categorical model of intensional computation is unique up to isomorphismServes as a stepping stone into research of computable categoriesIn addition to its early chapters introducing computability for beginners, this flexible textbook/resource also contains both middle chapters that expand for suitability to a graduate course as well as final chapters opening up new research. Dusko Pavlovic is a professor at the Department of Information and Computer Sciences at the University of Hawaii at Manoa, and by courtesy at the Department of Mathematics and the College of Engineering. He completed this book as an Excellence Professor at Radboud University in Nijmegen, The Netherlands.

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations.

This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability; and the art of computability, a skill to be practiced but also important in an esthetic sense of beauty and taste in mathematics.

This book presents a theory of apartness encompassing both point-set topology and the theory of uniform spaces. The first book on the apartness approach to constructive topology, it is a valuable addition to the literature on topology in computer science.

This book questions the relevance of computation to the physical universe.

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

This book questions the relevance of computation to the physical universe.