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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 machine- and Gödel number-oriented classical approaches, Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists and more applicable to practical programming problems.<br /> <br /> According to Jones, the fields of computability and complexity theory, as well as programming languages and semantics, have a great deal to offer each other. Computability and complexity theory have a breadth, depth, and generality not often seen in programming languages. The programming language community, meanwhile, has a firm grasp of algorithm design, presentation, and implementation. In addition, programming languages sometimes provide computational models that are more realistic in certain crucial aspects than traditional models.<br /> <br /> New results in the book include a proof that constant time factors do matter for its programming-oriented model of computation. (In contrast, Turing machines have a counterintuitive "constant speedup" property: that almost any program can be made to run faster, by any amount. Its proof involves techniques irrelevant to practice.) Further results include simple characterizations in programming terms of the central complexity classes PTIME and LOGSPACE, and a new approach to complete problems for NLOGSPACE, PTIME, NPTIME, and PSPACE, uniformly based on Boolean programs.<br /> <br /> Foundations of Computing series

Neil Deaton Jones is a retired Professor of Computer Science at the University of Copenhagen.

Introduction
3

The WHILE Language
27

Programs as Data Objects
47

Universal Programs for WHILE and I
69

Metaprogramming Selfapplication and Compiler Generation
89

Other Sequential Models of Computation
111

Robustness of Computability
127

Some Natural Unsolvable Problems
151

Overview of Complexity Theory
239

Time Usage of Treemanipulating Programs
261

Linear and Other Time Hierarchies for WHILE Programs
285

Spacebounded Computations
315

Nondeterministic Computations
331

Characterizations of LOGSPACE and PTIME by GOTO Programs
349

Completeness and Reduction of One Problem to Another
365

Complete Problems for PTIME
383

Hilberts Tenth Problem by M H Serensen
167

Inference Systems and Godels Incompleteness Theorem
187

Computability Theory Based on Numbers
205

More Abstract Approaches to Computability
215

Complete Problems for NPTIME
397

Appendix
412

Bibliography
447
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