C. S. Calude, G. Paun (eds.). Finite vs Infinite, Contributions to an Eternal Dilemma,
SpringerVerlag, London, 2000, ISBN: 1852332514. £45.00 March 2000, x + 372
pages softcover.
The finiteinfinite interplay is central in the human thinking, from ancient
philosophers and mathematicians (Zenon, Pythagoras), to modern mathematics (Cantor, Hilbert) and
computer science (Turing, Goedel). Recent developments in mathematics and computer science suggest
radically new answers to classical questions such as:

Does infinity exist?

Where does infinity come from?

How can we reconcile the finiteness of the human brain with the infinity
of ideas it produces?
These recent developments also open up new questions of debate, including:
 What is the role played by randomness?
 Are computers capable of handling the infinite through unconventional
media of computation?
 How can one approximate efficiently the finite by the infinite, and
conversely the infinite by the finite?
Wellknown authors from around the world, many of them architects of the mathematics and
computer science for the new century, contribute to this volume. While mathematical in spirit,
contributions have many connections with computer science, cognitive science, linguistics,
philosophy, physics, biology and semiotics.
 Preface
 Tribute to Professor Solomon Marcus
 Umberto Amato, Dan Tudor Vuza
Smoothing Data: When Finite and Infinite Dimensional
Help Each Other
 Hari Bercovici
Rearrangements of Real Functions Derived from
the Combinatorics of Young Tableaux
 Massimo Borelli, Andrea Sgarro
A Possibilistic Distance for Sequences of Equal
and Unequal Length
 Cristian S. Calude, Helmut Jürgensen, Shane Legg
Solving Problems with Finite Test Sets
 Cezar Câmpeanu, Kai Salomaa, Sheng Yu
State Complexity of Regular Languages: Finite Versus
Infinite
 Gregory J. Chaitin
A Century of Controversy over the Foundations of
Mathematics
 Florin Diacu
Finite Versus Infinite in Singularity Dynamics
 John Ewing, Ciprian Foias
An Interesting Serendipitous Real Number
 Rudolf Freund, Alexandru Mateescu, Arto Salomaa
Algebraic Representations of Regular Array Languages
 Salvatore Greco, Benedetto Matarazzo, Roman Slowinski
Rough Set Processing of Vague Information Using Fuzzy
Similarity Relations
 Tom Head
Relativized Code Concepts and MultiTube DNA
Dictionaries
 Lucian Ilie, Ion Petre, Grzegorz Rozenberg
Uniformly Scattered Factors
 Vincenzo Manca
Splicing Normalization and Regularity
 Carlos MartínVide
Infinitely Many Infinities
 Georges Nicolas
Finite and Infinite in Geography
 Piergiorgio Odifreddi
Ultrafilters, Dictators, and Gods
 Sergiu Rudeanu
On the Behaviour of Semiautomata
 Jouko Seppänen
Infinity  An Outline of Conceptions in Mythology,
Cosmology and Natural Philosophy
 Hava T. Siegelmann
Finite Versus Infinite Neural Computation
 Dan A. Simovici, Szymon Jaroszewicz
On InformationTheoretical Aspects of Relational Databases
 Robert M. Solovay
A Version of W for Which ZFC Cannot Predict a Single
Bit
 Ludwig Staiger
On the Power of Reading the Whole Infinite Input Tape
 Victor Vianu
Finite and Infinite in Logic