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

by Gazeau, Jean-Pierre; Nesetril, Jaroslav; Rovan, Branislav

• ISBN13: 9781586037062
• ISBN10: 1586037064
• Format: Hardcover
• Copyright: 2007-02-01
• Publisher: Ios Pr Inc

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 theory	p. 3
Dynamical symmetry approach to entanglement	p. 25
Mathematics of phase transitions	p. 55
The topology of deterministic chaos : stretching, squeezing and linking	p. 71
Random fractals	p. 91
Quasicrystals : algebraic, combinatorial and geometrical aspects	p. 113
Pisot number system and its dual tiling	p. 133
Non-standard number representation : computer arithmetic, beta-numeration and quasicrystals	p. 155
An introduction to the theory of finite transducers	p. 171
Generating languages	p. 189
Basic enumerative combinatorics	p. 211
An introduction to noncommutative symmetric functions	p. 231
An introduction to combinatorial Hopf algebras - examples and realizations	p. 253
Complex networks : deterministic models	p. 275
Homomorphisms of structures concepts and highlight	p. 295
Some discrete tools in statistical physics	p. 317
Table of Contents provided by Blackwell. All Rights Reserved.