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9781586037062

Physics and Theoretical Computer Science : From Numbers and Languages to (Quantum) Cryptography Security

by ; ;
  • ISBN13:

    9781586037062

  • ISBN10:

    1586037064

  • Format: Hardcover
  • Copyright: 2007-02-01
  • Publisher: Ios Pr Inc

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Summary

The goal of this publication is to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. The intersection of combinatorics and statistical physics has been an area of great activity over the past few years, fertilized by an exchange not only of techniques but of objectives as well. Some of the topics of particular interest are: percolation, random coloring, mixing, homomorphisms from and to fixed graph, phase transitions, threshold phenomena. This book is aimed to assemble theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn more about recent developments in cryptography, algorithmics, symbolic calculus, non-standard numeration systems, algebraic combinatorics, automata etc., which could reveal themselves to be of crucial interest in natural sciences. This volume is organized along the following rough thematic division: Physics; Chaos and Fractals; Quasi-Crystals and Tilings; Numeration, Automata, and Languages; Algebraic Combinatorics; and Graphs and Networks.

Table of Contents

Mathematical aspects of quantum information theoryp. 3
Dynamical symmetry approach to entanglementp. 25
Mathematics of phase transitionsp. 55
The topology of deterministic chaos : stretching, squeezing and linkingp. 71
Random fractalsp. 91
Quasicrystals : algebraic, combinatorial and geometrical aspectsp. 113
Pisot number system and its dual tilingp. 133
Non-standard number representation : computer arithmetic, beta-numeration and quasicrystalsp. 155
An introduction to the theory of finite transducersp. 171
Generating languagesp. 189
Basic enumerative combinatoricsp. 211
An introduction to noncommutative symmetric functionsp. 231
An introduction to combinatorial Hopf algebras - examples and realizationsp. 253
Complex networks : deterministic modelsp. 275
Homomorphisms of structures concepts and highlightp. 295
Some discrete tools in statistical physicsp. 317
Table of Contents provided by Blackwell. All Rights Reserved.

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