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

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Computability978-1-4612-0863-1Series ISSN 0072-5285 Series E-ISSN 2197-5612

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https://doi.org/10.1007/978-3-642-22958-9dictive activity. However, that activity is not the object of this book, which is to investigate the ., rather than the practice, of computation. That investigation is based upon the notion of a partial function computed by a Turing machine, to which we now turn our attention.

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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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Computable Partial Functions,dictive activity. However, that activity is not the object of this book, which is to investigate the ., rather than the practice, of computation. That investigation is based upon the notion of a partial function computed by a Turing machine, to which we now turn our attention.

領(lǐng)帶

,Rice’s Theorem and the Recursion Theorem,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.

LUDE

Sanvesh Srivastava,Rebecca W. DoergeThroughout 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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Columbia University Statistics,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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https://doi.org/10.1007/978-3-642-22958-9Is 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?

短程旅游

Bending of Curved Bars and Rigid Frames,We begin this chapter by studying in some detail a proof of the fundamental result of computability theory: the undecidability of the halting problem. This will lead us into a discussion of computable real numbers, .-ary expansions, and the elements of computable analysis. You are encouraged to limber up by trying the following exercises.