Cristian S. Calude's Books

Information and Randomness

An Algorithmic Perspective

By: Cristian S. Calude

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Information and Randomness

An Algorithmic Perspective

By: Cristian S. Calude

The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

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481

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662049783

ISBN 13

9783662049785

Finite Versus Infinite

Contributions to an Eternal Dilemma

By: Cristian S. Calude,Gheorghe Paun

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Finite Versus Infinite

Contributions to an Eternal Dilemma

By: Cristian S. Calude,Gheorghe Paun

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.

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Page Count

376

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447107519

ISBN 13

9781447107514

To Halt Or Not To Halt? That Is The Question

By: Cristian S Calude

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To Halt Or Not To Halt? That Is The Question

By: Cristian S Calude

This is a book about the 'Halting Problem', arguably the most (in)famous computer-related problem: can an algorithm decide in finite time whether an arbitrary computer program eventually stops? This seems a dull, petty question: after all, you run the program and wait till it stops. However, what if the program does not stop in a reasonable time, a week, a year, or a decade? Can you infer that it will never stop? The answer is negative. Does this raise your interest? If not, consider these questions: Can mathematics be done by computers only? Can software testing be fully automated? Can you write an anti-virus program which never needs any updates? Can we make the Internet perfectly secure? Your guess is correct: the answer to each question is negative. The Halting Problem is 'hidden' in many subjects, from logic (is mathematics free of contradictions?), physics (is quantum randomness perfect?), to philosophy (do humans have free will, or do our brains generate our thoughts and decisions in a deterministic way?) and quantum computing (why we don't have a quantum Halting Problem?) — this book will visit each of them.Written in an informal and thought-provoking language, supported with suggestive illustrations and applications and almost free of arcane mathematics (formal arguments are relegated to particular parts dedicated to the mathematically-oriented reader), the book will stimulate the curiosity and participation of the reader interested in the consequences of the limits of computing and in various attempts to cope with them.

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Page Count

332

Publisher

World Scientific

Published Date

ISBN 10

9811232296

ISBN 13

9789811232299

Discrete Mathematics and Theoretical Computer Science

4th International Conference, DMTCS 2003, Dijon, France, July 7-12, 2003. Proceedings

By: Cristian S. Calude,Michael J. Dinneen

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Discrete Mathematics and Theoretical Computer Science

4th International Conference, DMTCS 2003, Dijon, France, July 7-12, 2003. Proceedings

By: Cristian S. Calude,Michael J. Dinneen

The fourthDiscrete Mathematics andTheoreticalComputer Science Conference (DMTCS 2003) was jointly organized by the Centre for Discrete Mathematics and Theoretical Computer Science (CDMTCS) of the University of Auckland and the University of Bourgogne in Dijon, France, and took place in Dijon from 7 to12 July2003.Thepreviousconferenceswereheld inAuckland,NewZealand (1996, 1999) and Constan ̧ ta, Romania (2001). The ?ve invited speakers of the conference were: G.J. Chaitin (IBM, New York), C. Ding (UST, Hong Kong), S. Istrail (Celera Genomics, Rockville), M. Margenstein (LITA, Metz), and T. Walsh (UQAM, Montreal). The Programme Committee, consisting of V. Berthe (Marseille), S. Boza- lidis(Thessaloniki),C.S.Calude(chair,Auckland),V.E.Cazanescu(Bucharest), F. Cucker (Hong Kong), M. Deza (Paris and Tokyo), J. Diaz (Spain), M.J. D- neen(secretary,Auckland),B.Durand(Marseille),L.Hemaspaandra(Rochester), P. Hertling (Hagen), J. Kohlas (Fribourg), G. Markowski (Orono), M. Mitrovic (Nis), A. Salomaa (Turku), L. Staiger (Halle), D. Skordev (So?a), G. Slutzki (Ames), I. Tomescu (Bucharest), M. Yasugi (Kyoto), and V. Vajnovszki (- jon), selected 18 papers (out of 35) to be presented as regular contributions and 1 5 other special CDMTCS papers.

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Page Count

310

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540405054

ISBN 13

9783540405054

Randomness and Complexity

From Leibniz to Chaitin

By: Cristian S. Calude,Gregory J. Chaitin

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Randomness and Complexity

From Leibniz to Chaitin

By: Cristian S. Calude,Gregory J. Chaitin

The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin''s 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s). Chapter 1: On Random and Hard-to-Describe Numbers (902 KB). Contents: On Random and Hard-to-Describe Numbers (C H Bennett); The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies); What is a Computation? (M Davis); A Berry-Type Paradox (G Lolli); The Secret Number. An Exposition of Chaitin''s Theory (G Rozenberg & A Salomaa); Omega and the Time Evolution of the n-Body Problem (K Svozil); God''s Number: Where Can We Find the Secret of the Universe? In a Single Number! (M Chown); Omega Numbers (J-P Delahaye); Some Modern Perspectives on the Quest for Ultimate Knowledge (S Wolfram); An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding (D Zeilberger); and other papers. Readership: Computer scientists and philosophers, both in academia and industry.

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466

Publisher

World Scientific

Published Date

ISBN 10

9812770836

ISBN 13

9789812770837

Computation, Physics and Beyond

International Workshop on Theoretical Computer Science, WTCS 2012, Dedicated to Cristian S. Calude on the Occasion of His 60th Birthday, Auckland, New Zealand, February 21-24, 2012, Revised Selected and Invited Papers

By: Michael J. Dinneen,Bakhadyr Khoussainov,Prof. Andre Nies,André Nies

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Computation, Physics and Beyond

By: Michael J. Dinneen,Bakhadyr Khoussainov,Prof. Andre Nies,André Nies

This Festschrift volume has been published in honor of Cristian Calude on the occasion of his 60th birthday and contains contributions from invited speakers and regular papers presented at the International Workshop on Theoretical Computer Science, WTCS 2012, held in Auckland, New Zealand, in February 2012. Cristian Calude has made a significant contribution to research in computer science theory. Along with early work by Chaitin, Kučera, Kurtz, Solovay, and Terwijn his papers published in the mid-1990s jointly with Khoussainov, Hertling, and Wang laid the foundation for the development of modern theory of algorithmic randomness. His work was essential for establishing the leading role of New Zealand in this area. The research interests of Cristian Calude are reflected in the topics covered by the 32 papers included in this book, namely: algorithmic information theory, algorithms, automata and formal languages, computing and natural sciences, computability and applications, logic and applications, philosophy of computation, physics and computation, and unconventional models of computation. They have been organized into four parts. The first part consists of papers discussing his life achievements. This is followed by papers in the three general areas of complexity, computability, and randomness; physics, philosophy (and logic), and computation; and algorithms, automata, and formal models (including unconventional computing).

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Page Count

436

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642276539

ISBN 13

9783642276538

Book's by Cristian S. Calude

Information and Randomness

Information and Randomness

Finite Versus Infinite

Finite Versus Infinite

To Halt Or Not To Halt? That Is The Question

To Halt Or Not To Halt? That Is The Question

Discrete Mathematics and Theoretical Computer Science

Discrete Mathematics and Theoretical Computer Science

Randomness and Complexity

Randomness and Complexity

Computation, Physics and Beyond

Computation, Physics and Beyond

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