'a clear and unifying treatment of fundamental concepts underlying Computer Sciences and Foundations of Mathematics' Professor Boris Zilber (Professor of Mathematical Logic, University of Oxford)

'an excellent book' Professor Dov Gabbay (King's College, London)

The ability to reason and think in a logical manner...

Computability and complexity theory should be of central concern to practitioners as well as theorists. Unfortunately, however, the field is known for its impenetrability. Neil Jones's goal as an educator and author is to build a bridge between computability and complexity theory and other areas of computer science, especially programming. In a...

It may sound surprising that in computing, a field which develops so fast that the future often becomes the past without having been the present, there is nothing more stable and worthwhile learning than its foundations.

It may sound less surprising that in a field with such a revolutionary methodological impact on all sciences and...

Computer Science: Reflections on the Field, Reflections from the Field provides a concise characterization of key ideas that lie at the core of computer science (CS) research. The book offers a description of CS research recognizing the richness and diversity of the field. It brings together two dozen essays on diverse aspects...

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are...

Before digital computers ever existed, Alan Turing envisioned their power and versatility...but also proved what computers could never do.

In an extraordinary and ultimately tragic life that unfolded like a novel, Turing helped break the German Enigma code to turn the tide of World War II, later speculated on...

Though we did not know it at the time, this book’s genesis began with
the arrival of Cris Calude in New Zealand. Cris has always had an intense
interest in algorithmic information theory. The event that led to much of
the recent research presented here was the articulation by Cris of a seemingly
innocuous question. This question...

The study of the class of computable partial functions (i.e., recursive partial functions)
stands at the intersection of three fields: mathematics, theoretical computer science,
and philosophy.

Mathematically, computability theory originates from the concept of an algorithm.
It leads to a classification of functions according...

This book provides an elementary introduction to formal languages and machine computation. The materials covered include computation-oriented mathematics, finite automata and regular languages, push-down automata and context-free languages, Turing machines and recursively enumerable languages, and computability and complexity. As integers are...

Hypercomputation is a relatively new theory of computation that is about computing methods and devices that transcend the so-called Church-Turing thesis. This book will provide a thorough description of the field of hypercomputation covering all attempts at devising conceptual hypermachines and all new promising computational paradigms that may...

This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, first-order, and Horn- clause logics, together with an analysis of the semantic aspects of the method. It is through the inference rule of resolution that both proofs and computations can be...

Presents an introduction to the basic models of computability to the undergraduate students. This book deals with Finite Automata and their properties. It provides a class of models and enables the analysis of context-free languages.

This book deals with a fascinating and important subject which has the
fundamentals of computer...