Feasible Mathematics

Author: S.R. Buss
Editor: Springer Science & Business Media
ISBN: 1461234662
File Size: 52,55 MB
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A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.
Feasible Mathematics
Language: en
Pages: 352
Authors: S.R. Buss, P.J. Scott
Categories: Computers
Type: BOOK - Published: 2013-03-07 - Publisher: Springer Science & Business Media

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm
Feasible Mathematics II
Language: en
Pages: 447
Authors: Peter Clote, Jeffrey B. Remmel
Categories: Computers
Type: BOOK - Published: 2013-03-13 - Publisher: Springer Science & Business Media

Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to
Proof Complexity and Feasible Arithmetics
Language: en
Pages: 320
Authors: Paul W. Beame, Samuel R. Buss
Categories: Mathematics
Type: BOOK - Published: - Publisher: American Mathematical Soc.

Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can
Reflections on the Foundations of Mathematics
Language: en
Pages:
Authors: Wilfried Sieg, Richard Sommer, Carolyn Talcott
Categories: Mathematics
Type: BOOK - Published: 2017-03-30 - Publisher: Cambridge University Press

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes
Reverse Mathematics 2001
Language: en
Pages: 401
Authors: Stephen G. Simpson
Categories: Mathematics
Type: BOOK - Published: 2017-03-30 - Publisher: Cambridge University Press

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Reverse mathematics is a program of research in the