Feasible Mathematics II

  • Peter Clote
  • Jeffrey B. Remmel

Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 13)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Stephen Bellantoni
    Pages 15-29
  3. Maria Luisa Bonet, Samuel R. Buss, Toniann Pitassi
    Pages 30-56
  4. Douglas Cenzer, Jeffrey Remmel
    Pages 91-153
  5. Rodney G. Downey, Michael R. Fellows
    Pages 219-244
  6. Mauricio Karchmer
    Pages 245-255
  7. Bakhadyr Khoussainov, Anil Nerode
    Pages 256-283
  8. Jan Krajíček
    Pages 284-319
  9. Alexander A. Razborov
    Pages 344-386
  10. Helmut Schwichtenberg, Stanley S. Wainer
    Pages 387-406
  11. Rineke Verbrugge
    Pages 429-447

About these proceedings

Introduction

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 come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa­ tion device, such as a 'lUring machine or boolean circuit. Feasible math­ ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa­ rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc­ ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.

Keywords

algebra combinatorics complexity logic mathematics

Editors and affiliations

  • Peter Clote
    • 1
  • Jeffrey B. Remmel
    • 2
  1. 1.Department of Computer ScienceBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSan Diego La JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2566-9
  • Copyright Information Birkhäuser Boston 1995
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7582-4
  • Online ISBN 978-1-4612-2566-9
  • About this book
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