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 shift away from the Turing machin...(展开全部)

Complexity theory is a central field of the theoretical foundations of computer science. It is concerned with the general study of the intrinsic complexity of computational tasks; that is, it addresses the question of what can be achieved within limited time (and/or with other limited natural computational resources). This book offers a conceptual perspective on complexity theo...(展开全部)

Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

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...(展开全部)

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 complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computab...(展开全部)

A text for a second course in logic for graduate and advanced undergraduate students. This third edition has been corrected and contains thoroughly revised versions of the chapters on Ramsey and provability, with new exercises provided for three other chapters. There are also two new chapters dealing with undecidable sentences and on the non-existence of non-standard recursive ...(展开全部)

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...(展开全部)

Now in its fourth edition, this book has become a classic because of its accessibility to students without a mathematical background, and because it covers not only 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. John Burgess has enha...(展开全部)

Preface Acknowledgments Dependency Graph 1 Preliminaries 1. Sets and n-tuples 2. Functions 3. Alphabets and Strings 4. Predicates 5. Quantifiers 6. Proof by Contradiction 7. Mathematical Induction Part 1 Cmnputability 2 Programs and Computable Functions 1. A Programming Language 2. Some Examples of Programs 3. Syntax - 4. Computable Functions 5. More about Macros 3 Primitive Re...(展开全部)

The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible t...(展开全部)