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Feasible Mathematics

A Mathematical Sciences Institute Workshop, Ithaca, New York, June 1989

  • Samuel R. Buss
  • Philip J. Scott

Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 9)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Stephen A. Cook, Bruce M. Kapron
    Pages 71-96
  3. John N. Crossley, J. B. Remmel
    Pages 99-130
  4. J. C. E. Dekker
    Pages 131-160
  5. Fernando Ferreira
    Pages 161-180
  6. John Foy, Alan R. Woods
    Pages 181-193
  7. Jean-Yves Girard, Andre Scedrov, Philip J. Scott
    Pages 195-209
  8. Yuri Gurevich
    Pages 211-219
  9. H. James Hoover
    Pages 221-237
  10. Jan Krajíček, Gaisi Takeuti
    Pages 259-280
  11. Anil Nerode, J. B. Remmel
    Pages 293-319
  12. Back Matter
    Pages 351-352

About this book

Introduction

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.

Keywords

Arithmetic Finite Parity algebra algorithms calculus complexity computer function mathematics pigeonhole principle recursion time

Editors and affiliations

  • Samuel R. Buss
    • 1
  • Philip J. Scott
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  2. 2.Department of MathematicsUniversity of OttawaOttawaCanada

Bibliographic information