A.J. Kfoury - Böcker

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.

Computer science seeks to provide a scientific basis for the study of inform a­ tion processing, the solution of problems by algorithms, and the design and programming of computers. The last forty 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 development of mathematical techniques to allow the rigorous specification of program, process, and machine. The present volume is one of a series, The AKM Series in Theoretical Computer Science, designed to make key mathe­ matical developments in computer science readily accessible to under­ graduate and beginning graduate students. Specifically, this volume takes readers with little or no mathematical background beyond high school algebra, and gives them a taste of a number of topics in theoretical computer science while laying the mathematical foundation for the later, more detailed, study of such topics as formal language theory, computability theory, programming language semantics, and the study of program verification and correctness. Chapter 1 introduces the basic concepts of set theory, with special emphasis on functions and relations, using a simple algorithm to provide motivation. Chapter 2 presents the notion of inductive proof and gives the reader a good grasp on one of the most important notions of computer science: the recursive definition of functions and data structures.