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E-raamat: Finite Versus Infinite: Contributions to an Eternal Dilemma

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Finite Versus Infinite: Contributions to an Eternal DilemmaSuurem pilt
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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.
Preface v Tribute to Professor Solomon Marcus vii Smoothing Data: When Finite and Infinite Dimensional Help Each Other 1(16) Umberto Amato Dan Tudor Vuza Rearrangements of Real Functions Derived from the Combinatorics of Young Tableaux 17(10) Hari Bercovici A Possibilistic Distance for Sequences of Equal and Unequal Length 27(12) Massimo Borelli Andrea Sgarro Solving Problems with Finite Test Sets 39(14) Cristian S. Calude Helmut Jurgensen Shane Legg State Complexity of Regular Languages: Finite Versus Infinite 53(22) Cezar Campeanu Kai Salomaa Sheng Yu A Century of Controversy over the Foundations of Mathematics 75(26) Gregory J. Chaitin Finite Versus Infinite in Singularity Dynamics 101(18) Florin Diacu An Interesting Serendipitous Real Number 119(8) John Ewing Ciprian Foias Algebraic Representations of Regular Array Languages 127(22) Rudolf Freund Alexandru Mateescu Arto Salomaa Rough Set Processing of Vague Information Using Fuzzy Similarity Relations 149(26) Salvatore Greco Benedetto Matarazzo Roman Slowinski Relativized Code Concepts and Multi-Tube DNA Dictionaries 175(12) Tom Head Uniformly Scattered Factors 187(12) Lucian Ilie Ion Petre Grzegorz Rozenberg Splicing Normalization and Regularity 199(18) Vincenzo Manca Infinitely Many infinities 217(14) Carlos Martin-Vide Finite and Infinite in Geography 231(8) Georges Nicolas Ultrafilters, Dictators, and Gods 239(8) Piergiorgio Odifreddi On the Behaviour of Semiautomata 247(10) Sergiu Rudeanu Infinity - An Outline of Conceptions in Mythology, Cosmology and natural Philosophy 257(28) Jouko Seppanen Finite Versus Infinite Neural Computation 285(16) Hava T. Siegelmann On Information-Theoretical Aspects of Relational Databases 301(22) Dan A. Simovici Szymon Jaroszewicz A Version of Ω for Which ZFC Cannot Predict a Single Bit 323(12) Robert M. Solovay On the Power of Reading the Whole Infinite Input Tape 335(14) Ludwig Staiger Finite and Infinite in Logic 349 Victor Vianu
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