Complexity and Real Computation
Authors: Blum, L., Cucker, F., Shub, M., Smale, S.
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- About this Textbook
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Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The objects of study are algorithms defined within a formal model of computation. Upper bounds on the computational complexity of a problem are usually derived by constructing and analyzing specific algorithms. Meaningful lower bounds on computational complexity are harder to come by, and are not available for most problems of interest. The dominant approach in complexity theory is to consider algorithms as oper ating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot rep resent real or complex numbers, unless the numbers are rounded to approximate values from a discrete set. A major concern of the theory is the number of com putation steps required to solve a problem, as a function of the length of the input string.
- Table of contents (23 chapters)
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Introduction
Pages 3-36
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Definitions and First Properties of Computation
Pages 37-68
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Computation over a Ring
Pages 69-81
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Decision Problems and Complexity over a Ring
Pages 83-98
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The Class NP and NP-Complete Problems
Pages 99-112
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Table of contents (23 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Complexity and Real Computation
- Authors
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- Lenore Blum
- Felipe Cucker
- Michael Shub
- Steve Smale
- Copyright
- 1998
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4612-0701-6
- DOI
- 10.1007/978-1-4612-0701-6
- Hardcover ISBN
- 978-0-387-98281-6
- Softcover ISBN
- 978-1-4612-6873-4
- Edition Number
- 1
- Number of Pages
- XVI, 453
- Topics
