Finite Versus Infinite

Contributions to an Eternal Dilemma

  • Cristian Calude
  • Gheorghe Păun

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Massimo Borelli, Andrea Sgarro
    Pages 27-38
  3. Cristian S. Calude, Helmut Jürgensen, Shane Legg
    Pages 39-52
  4. Cezar Câmpeanu, Kai Salomaa, Sheng Yu
    Pages 53-73
  5. John Ewing, Ciprian Foias
    Pages 119-126
  6. Rudolf Freund, Alexandru Mateescu, Arto Salomaa
    Pages 127-148
  7. Salvatore Greco, Benedetto Matarazzo, Roman Slowinski
    Pages 149-173
  8. Lucian Ilie, Ion Petre, Grzegorz Rozenberg
    Pages 187-198
  9. Vincenzo Manca
    Pages 199-215
  10. Carlos Martín-Vide
    Pages 217-230
  11. Georges Nicolas
    Pages 231-237
  12. Piergiorgio Odifreddi
    Pages 239-245
  13. Sergiu Rudeanu
    Pages 247-256
  14. Hava T. Siegelmann
    Pages 285-299

About this book

Introduction

The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe­ matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com­ puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

Keywords

Algebra Automata Theory Cantor Finite Mathematical Logic Neural Computing Problem-solving combinatorics complexity databases function logic mathematics

Authors and affiliations

  • Cristian Calude
    • 1
  • Gheorghe Păun
    • 2
  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.Institute of MathematicsRomanian Academy of SciencesBucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0751-4
  • Copyright Information Springer-Verlag London 2000
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-251-8
  • Online ISBN 978-1-4471-0751-4
  • About this book