A Programming Approach to Computability (Monographs in Computer Science)

About this book

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 todays 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.