In 1936, before the development of modern computers, Alan Turing proposed the concept of a machine that would embody the interaction of mind, machine, and logical instruction. The idea of a ``universal machine’’ inspired the notion of programs stored in a computer’s memory. Nowadays, the study of computable functions is a core topic taught to mathematics and computer science undergraduates.
Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation. It begins with the definition of a computable function and an algorithm, and discusses decidability, enumerability, universal functions, numberings and their properties, $m$-completeness, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees of unsolvability. The authors complement the main text with over 150 problems. They also cover specific computational models, such as Turing machines and recursive functions. The intended audience includes undergraduate students majoring in mathematics or computer science, and all mathematicians and computer scientists that would like to learn basics of the general theory of computation. The book is also an ideal reference source for designing a course.
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See also
- Software Exorcism: A Handbook for Debugging and Optimizing Legacy Code by Bill Blunden (2003)
- Hormones and the Endocrine System: Textbook of Endocrinology by Bernhard Kleine (2016)
- Genetics: A Conceptual Approach 6e by Benjamin A. Pierce (2017)
- A Functional Approach to Java by Ben Weidig (2022)
- Calculus of variations and optimal control by Amol Sasan (2005)