Titlebook: Computability; A Mathematical Sketc Douglas S. Bridges Textbook 1994 Springer Science+Business Media New York 1994 complexity.computability

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Preliminaries,Throughout this book we assume familiarity with the standard notations and basic results of informal set theory, as found in [18]. We use the following notation for sets of numbers.

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What Is a Turing Machine?,We begin our study of computability by describing one of the earliest mathematical models of computation, one for which the underlying informal picture is especially easy to understand—the Turing machine.

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Effective Enumerations,Is every subset of . the domain of some computable partial function? If not, can we characterise those subsets of . that are domains of computable partial functions?

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,Beams—Shear Force and Bending Moment,eory. The first of these, Rice’s Theorem, characterises a large class of nonrecursive subsets of .; the second, the Recursion Theorem, has many applications, some of which appear at the end of this chapter, and some, in perhaps unexpected contexts, in later chapters.

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