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A Programming Approach to Computability (Paperback, Softcover reprint of the original 1st ed. 1982)
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A Programming Approach to Computability (Paperback, Softcover reprint of the original 1st ed. 1982)
Series: Monographs in Computer Science
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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."
General
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