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Finite Versus Infinite

Contributions to an Eternal Dilemma

  • Book
  • © 2000

Overview

Authors:
  1. Cristian Calude

    1. Department of Computer Science, University of Auckland, Auckland, New Zealand

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  2. Gheorghe Păun

    1. Institute of Mathematics, Romanian Academy of Sciences, Bucharest, Romania

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Smoothing Data: When Finite and Infinite Dimensional Help Each Other

    • Umberto Amato, Dan Tudor Vuza
    Pages 1-16

  3. Rearrangements of Real Functions Derived from the Combinatorics of Young Tableaux

    • Hari Bercovici
    Pages 17-26

  4. A Possibilistic Distance for Sequences of Equal and Unequal Length

    • Massimo Borelli, Andrea Sgarro
    Pages 27-38

  5. Solving Problems with Finite Test Sets

    • Cristian S. Calude, Helmut Jürgensen, Shane Legg
    Pages 39-52

  6. State Complexity of Regular Languages: Finite versus Infinite

    • Cezar Câmpeanu, Kai Salomaa, Sheng Yu
    Pages 53-73

  7. A Century of Controversy over the Foundations of Mathematics

    • Gregory J. Chaitin
    Pages 75-100

  8. Finite Versus Infinite in Singularity Dynamics

    • Florin Diacu
    Pages 101-117

  9. An Interesting Serendipitous Real Number

    • John Ewing, Ciprian Foias
    Pages 119-126

  10. Algebraic Representations of Regular Array Languages

    • Rudolf Freund, Alexandru Mateescu, Arto Salomaa
    Pages 127-148

  11. Rough Set Processing of Vague Information Using Fuzzy Similarity Relations

    • Salvatore Greco, Benedetto Matarazzo, Roman Slowinski
    Pages 149-173

  12. Relativized Code Concepts and Multi-Tube DNA Dictionaries

    • Tom Head
    Pages 175-186

  13. Uniformly Scattered Factors

    • Lucian Ilie, Ion Petre, Grzegorz Rozenberg
    Pages 187-198

  14. Splicing Normalization and Regularity

    • Vincenzo Manca
    Pages 199-215

  15. Infinitely Many Infinities

    • Carlos Martín-Vide
    Pages 217-230

  16. Finite and Infinite in Geography

    • Georges Nicolas
    Pages 231-237

  17. Ultrafilters, Dictators, and Gods

    • Piergiorgio Odifreddi
    Pages 239-245

  18. On the Behaviour of Semiautomata

    • Sergiu Rudeanu
    Pages 247-256

  19. Infinity — An Outline of Conceptions in Mythology, Cosmology and Natural Philosophy

    • Jouko Seppänen
    Pages 257-283

  20. Finite Versus Infinite Neural Computation

    • Hava T. Siegelmann
    Pages 285-299
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Computer Science, University of Auckland, Auckland, New Zealand

    Cristian Calude

  • Institute of Mathematics, Romanian Academy of Sciences, Bucharest, Romania

    Gheorghe Păun

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