Ebook: A Programming Approach to Computability
- Genre: Computers // Programming
- Tags: Applications of Mathematics, Computation by Abstract Devices, Software Engineering
- Series: Texts and Monographs in Computer Science
- Year: 1982
- Publisher: Springer
- Language: English
- pdf
Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today's computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop ment of mathematical techniques to allow the rigorous specification of program, process, and machine.
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-16
The Syntax and Semantics of while-Programs....Pages 17-44
Enumeration and Universality of the Computable Functions....Pages 45-74
Techniques of Elementary Computability Theory....Pages 75-94
Program Methodology....Pages 95-137
The Recursion Theorem and Properties of Enumerations....Pages 138-151
Computable Properties of Sets (Part 1)....Pages 152-175
Computable Properties of Sets (Part 2)....Pages 176-195
Alternative Approaches to Computability....Pages 196-234
Back Matter....Pages 235-253
Content:
Front Matter....Pages i-viii
Introduction....Pages 1-16
The Syntax and Semantics of while-Programs....Pages 17-44
Enumeration and Universality of the Computable Functions....Pages 45-74
Techniques of Elementary Computability Theory....Pages 75-94
Program Methodology....Pages 95-137
The Recursion Theorem and Properties of Enumerations....Pages 138-151
Computable Properties of Sets (Part 1)....Pages 152-175
Computable Properties of Sets (Part 2)....Pages 176-195
Alternative Approaches to Computability....Pages 196-234
Back Matter....Pages 235-253
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