Gheorghe Paun

Cristian S. Calude

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.

Contributions to an Eternal Dilemma

Finite Versus Infinite

Michael J. Dinneen

Elena Calude

This book constitutes the refereed proceedings of the 8th International Conference on Developments in Language Theory, DLT 2004, held in Auckland, New Zealand in December 2004. The 30 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 47 submissions. The main subjects are formal languages, automata, conventional and unconventional computation theory, and applications of automata theory. Among the topics addressed are grammars and acceptors for strings, graphs, and arrays; efficient text algorithms, combinatorial and algebraic properties of languages; decision problems; relations to complexity theory and logic; picture description and analysis; cryptography; concurrency; DNA computing; and quantum computing.

8th International Conference, DLT 2004, Auckland, New Zealand, December 13-17, Proceedings

Developments in Language Theory

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.

An Algorithmic Perspective

Information and Randomness

Grzegorz Rozenberg

Arto Salomaa

This volume is dedicated to Hermann Maurer on his 70th birthday. Topics include Automata, Formal Languages and Computability to various aspects of the Practice of Computer Science, as well as from Algorithmics to Learning.

Essays Dedicated to Hermann Maurer on the Occasion of His 70th Birthday

Rainbow of Computer Science

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.

From Leibniz to Chaitin

Randomness and Complexity

Rūsiņš Freivalds

Iwama Kazuo

Professor Jozef Gruska is a well known computer scientist for his many and broad results. He was the father of theoretical computer science research in Czechoslovakia and among the first Slovak programmers in the early 1960s. Jozef Gruska introduced the descriptional complexity of grammars, automata, and languages, and is one of the pioneers of parallel (systolic) automata. His other main research interests include parallel systems and automata, as well as quantum information processing, transmission, and cryptography. He is co-founder of four regular series of conferences in informatics and two in quantum information processing and the Founding Chair (1989-96) of the IFIP Specialist Group on Foundations of Computer Science.

Essays Dedicated to Jozef Gruska on the Occasion of His 80th Birthday

Computing with New Resources

Selim G. Akl

H. Todd Wareham

There is a world beyond Turing, as more and more computer researchers are demonstrating, but where would you find out about the current leading edge in unconventional computation? Here, in this fascinating work that is the refereed proceedings of the 6th International Conference on Unconventional Computation, held in Kingston, Canada, in August 2007. The 17 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. All current aspects of unconventional computation are addressed.

6th International Conference, UC 2007, Kingston, Canada, August 13-17, 2007, Proceedings

Unconventional Computation

Susan Stepney

This book constitutes the refereed proceedings of the 5th International Conference on Unconventional Computation, UC 2006, held in York, UK, in September 2006. The 17 revised full papers presented together with four invited full papers were carefully reviewed and selected for inclusion in the book. All current aspects of unconventional computation are addressed - theory as well as experiments and applications.

5th International Conference, UC 2006, York, UK, September 4-8, 2006, Proceedings

Ion Petre

Jarkko Kari

This book constitutes the refereed proceedings of the 10th International Conference on Unconventional Computation, UC 2011, held in Turku, Finland, in June 2011. The 17 revised full papers presented together with 6 extended abstracts of invited talks, and 3 extended abstracts of tutorials were carefully reviewed and selected from 33 initial submissions. The papers are devoted to all aspects of unconventional computation theory as well as experiments and applications. Typical topics are: natural computing including quantum, cellular, molecular, membrane, neural, and evolutionary computing, as well as chaos and dynamical system-based computing, and various proposals for computational mechanisms that go beyond the Turing model.

10th International Conference, UC 2011, Turku, Finland, June 6-10, 2011. Proceedings

Vincent Vajnovszki

The refereed proceedings of the 4th International Conference on Discrete Mathematics and Theoretical Computer Science, DMTCS 2003, held in Dijon, France, in July 2003. The 18 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 35 submissions. A broad variety of topics in discrete mathematics and the theory of computing is addressed including information theory, coding, algorithms, complexity, automata, computational mathematics, combinatorial computations, graph computations, algorithmic geometry, relational methods, game-theoretic methods, combinatorial optimization, and finite state systems.

Cristian S. Calude

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