Physics and Theoretical Computer Science: From Numbers and Languages to

349 Pages·2007·38.625 MB·

by  J.-P. Gazeau, J. Nesetril and B. Rovan, Editors

PHYSICS AND THEORETICAL COMPUTER SCIENCE
NATO Security through Science Series
This Series presents the results of scientific meetings supported under the NATO Programme for
Security through Science (STS).
Meetings supported by the NATO STS Programme are in security-related priority areas of
Defence Against Terrorism or Countering Other Threats to Security. The types of meeting
supported are generally “Advanced Study Institutes” and “Advanced Research Workshops”. The
NATO STS Series collects together the results of these meetings. The meetings are co-organized
by scientists from NATO countries and scientists from NATO’s “Partner” or “Mediterranean
Dialogue” countries. The observations and recommendations made at the meetings, as well as
the contents of the volumes in the Series, reflect those of participants and contributors only; they
should not necessarily be regarded as reflecting NATO views or policy.
Advanced Study Institutes (ASI) are high-level tutorial courses to convey the latest
developments in a subject to an advanced-level audience.
Advanced Research Workshops (ARW) are expert meetings where an intense but informal
exchange of views at the frontiers of a subject aims at identifying directions for future action.
Following a transformation of the programme in 2004 the Series has been re-named and re-
organised. Recent volumes on topics not related to security, which result from meetings
supported under the programme earlier, may be found in the NATO Science Series.
The Series is published by IOS Press, Amsterdam, and Springer Science and Business Media,
Dordrecht, in conjunction with the NATO Public Diplomacy Division.
Sub-Series
A. Chemistry and Biology Springer Science and Business Media
B. Physics and Biophysics Springer Science and Business Media
C. Environmental Security Springer Science and Business Media
D. Information and Communication Security IOS Press
E. Human and Societal Dynamics IOS Press
http://www.nato.int/science
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Sub-Series D: Information and Communication Security – Vol. 7 ISSN: 1574-5589
Physics and Theoretical Computer
Science
From Numbers and Languages to (Quantum) Cryptography
Edited by
Jean-Pierre Gazeau
APC, Université Paris 7-Denis Diderot, Paris, France
Jaroslav Nešetřil
Department of Applied Mathematics and ITI, MFF, Charles University,
Prague, Czech Republic
and
Branislav Rovan
Department of Computer Science, Comenius University, Bratislava, Slovakia
Amsterdam • Berlin • Oxford • Tokyo • Washington, DC
Published in cooperation with NATO Public Diplomacy Division
Proceedings of the NATO Advanced Study Institute on Emerging Computer Security
Technologies
Cargese, Corsica, France
17–29 October 2005
© 2007 IOS Press.
All rights reserved. No part of this book may be reproduced, stored in a retrieval system,
or transmitted, in any form or by any means, without prior written permission from the publisher.
ISBN 978-1-58603-706-2
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PRINTED IN THE NETHERLANDS
PhysicsandTheoreticalComputerScience v
J.-P.Gazeauetal.(Eds.)
IOSPress,2007
(cid:2)c 2007IOSPress.Allrightsreserved.
Preface
AsapartoftheNATOSecurityThroughScienceProgramme,thegoaloftheAdvanced
Study Institute Physics and Computer Science was to reinforce the interface between
physicalsciences,theoreticalcomputerscience,anddiscretemathematics.
NoonecandisputethecurrentimportanceofappliedaswellastheoreticalComputer
Science in the developmentand the practiceof PhysicalSciences. Physicists of course
usecomputersincommunicationaswellasinteachingtasksandresearch:softwarefor
symboliccalculus,dataprocessing,programming,modelingandnumericalsimulations,
learningandteachingwiththeaidofcomputers...
On the other hand, and besides the fundamental role played by mathematics in
physics,methodsimportedfromcomputerscienceareofincreasingimportanceintheo-
reticalphysics:algorithmics,symboliccalculus,non-standardnumerationsystems,alge-
braiccombinatorics,automata,cryptography... Some ofthem,like numeration,tilings
and their associated dynamical systems, algebraic combinatorics, have already played
animportantroleinrecentdevelopmentsinphysics,likethoseaccompanyingtheemer-
genceof new materials(e.g.quasicrystals, uncommensuratestructures)or the research
aroundquantuminformationand cryptography(entanglement),or yetaroundquantum
spin systems and related questions of integrability, and more generally in statistical
physics. The intersection of combinatorics and statistical physics has been an area of
greatactivityoverthe pastfew years,fertilized byan exchangenotonlyof techniques
butofobjectives.Spurredbycomputingtheoreticiansinterestedinapproximationalgo-
rithms,statisticalphysicistsanddiscretemathematicianshaveovercomelanguageprob-
lemsandfoundawealthofcommongroundinprobabilisticandalgebraiccombinatorics.
Close connectionsbetween percolationand randomgraphs,between graphmorphisms
and hard-constraintmodels, andbetween slow mixing andphase transition haveled to
newresultsandnewperspectives.Theseconnectionscanhelpinunderstandingtypical,
as opposed to extremal, behavior of combinatorial phenomena such as graph coloring
andhomomorphisms.Someofthetopicsofparticularinterestare:percolation,random
coloring,mixing,homomorphismsfromandtofixedgraph,phasetransitions,threshold
phenomena.
Hence, this NATO ASI School was aimed at assembling theoretical physicists
and specialists of theoretical informatics and discrete mathematics in order to learn
moreaboutrecentdevelopmentsincryptography,algorithmics,symboliccalculus,non-
standardnumerationsystems, algebraiccombinatorics,automata...which couldreveal
themselvestobeofcrucialinterestinnaturalsciences.Inturn,theSchoolofferedspecial-
istsinstatisticalphysicsordynamicalsystemsorinquantuminformationandquantum
cryptography,or yet in new materials (e.g. quasicrystals, uncommensuratestructures),
theopportunitytodescribeaspectsoftheirresearchinwhichnewapproachesimported
fromcomputerscienceareparticularlyneeded.
Therefore,nearly70participants(students+lecturers+organizers),comingfrom20
differentcountries(actuallymorethan25nationalities),mostofthembeingPhDstudents
or in post-doctoralpositions workingin variousfields, have attended courses givenby
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16 specialists in algorithmics,numerationsystems, algebraic combinatorics,automata,
languages,cryptography,quantuminformation,graphsandstatisticalmechanics.
Generally,thelectureshavebeenintroductoryandpedagogical.Theyperfectlycom-
plied with the objectiveofa realtransmission ofknowledgebetween the variouscom-
munitiesattendingtheInstitute.
During the ten working days of the School, a total of 40 hours was reserved for
lectures, and two half days were devoted to short presentations (30 or 45 min) mainly
byyoungresearchersandPhDparticipants.Around35participantspresentedtheirown
research on posters displayed during the whole duration of the School. The list of
participantsisgivenintheannexofthisbook.
ThreeLecturesandoneconcertwereorganizedwiththesupportoftheInstitutSci-
entifiquedeCargèse:
• RomanOPALKA,Artist,France,Poland,TheRiverofTime,
• PierreSIMONNET,UniversitédeCorse,Automataandgames,
• Jaroslav NEŠETRˇILandXavier VIENNOT,ArbresetFormes, ArtetMathéma-
tiques,
• Maria COLOMÉ (flute) and Jean-Yves THIBON (piano): Sonate, F. Poulenc,
Sonateensimineur,J.S.Bach.
They were aimed to attract a wide audience from Cargèse region. Moreover, the
pupilsoftheCargèseprimaryschoolenjoyedtwopedagogicalandplayfulpresentations
ofthecombinatoricsoftrees.
During the last auditorium meeting, the participants discussed important question
of the relations, on a pedagogical as well as institutional level, between physics and
computerscienceinhighereducation.
Thisvolumeisorganizedalongthefollowingroughthematicdivisions:
• Physics,
• ChaosandFractals,
• Quasi-CrystalsandTilings,
• Numeration,Automata,andLanguages,
• AlgebraicCombinatorics,
• GraphsandNetworks.
Acknowledgements
This NATO-ASI “PHYSICS AND COMPUTER SCIENCE” has also been supported
by l’ITI-DIMATIA, Charles University, Prague, the Collectivité Territoriale de Corse
(Corsica Region),the French Ministry of Foreign Affairs, the University of Marne-La-
ValléeandtheGDR673(CNRS)“Algorithmique,LangageetProgrammation”.
Jean-PierreGazeau,JaroslavNešetˇril,andBranislavRovan
Co-directorsoftheAdvancedStudyInstitutePhysicsandComputerScience
vii
Lecturers & Participants
◦
NATO-ASI N 981339
1. ABDAL-KADERGamal
Al-AzharUniversity,Cairo,Egypt
2. AKIYAMAShigeki
NiigataUniversity,Japan
3. AMBROZPetr
UniversitéParis7-DenisDiderot,France
4. ANDRLEMiroslav
AstonUniversity,Birmingham,UK
5. AUDENAERTKoenraadM.R.
ImperialCollege,London,UK
6. BALKOVALubomira
CzechTechnicalUniversity,Prague,CzechRepublic
7. BANDTChristoph
Ernst-Moritz-Arndt-Universitaet,Greifswald,Germany
8. BERNATJulien
UniversitédelaMéditerranée,Marseille,France
9. BERTIStefano
UniversitàdiTorino,Italy
10. BISTAGNINOAndrea
UniversitàdiTorino,Italy
11. BUCHAViktar
NationalAcademyofSciencesofBelarus,Minsk,Belarus
12. CARAMETELaurentiu-Ioan
InstituteofSpaceScience,Bucharest-Magurele,Romania
13. CHIDongPyo
SeoulNationalUniversity,Korea
14. COLOMÉTatchéMaria
UniversitéParis-Sud,Orsay,France
15. COMELLASFrancesc
UniversitatPolitecnicadeCatalunya,Barcelona,Spain
16. DALFÓCristina
UnivertitatPolitècnicadeCatalunya,Barcelona,Spain
17. DEMIERAnna
UniversityofOxford,UK
18. DESOUZARodrigo
EcoleNationaleSupérieuredesTélécommunications,Paris,France
19. DMITROCHENKOOleg
BryanskStateTechnicalUniversity,Russia
viii
20. DONCHENKOLyudmyla
DonetskStateMedicineUniversity,Ukraine
21. FROUGNYChristiane
UniversitéParis7-DenisDiderotandUniversitéParis8,France
22. GADJIEVBahruz
SAMInternationalUniversityofNature,SocietyandMan,Dubna,Russia
23. GAJJARPankajkumar
SardarPatelUniversity,Gujarat,India
24. GARCIADELEONPedro
UniversitédeMarne-la-Vallée,France
25. GARNERONESilvano
QuantumComputationISIFoundation,Torino,Italy
26. GAZEAUJean-Pierre
UniversitéParis7-DenisDiderot,France
27. GOLINSKITomasz
UniversityofBialystok,Poland
28. HADAROfer
Ben-GurionUniversityoftheNegev,Beer-Sheva,Israel
29. HIVERTFlorent
UniversitédeRouen,France
30. HONNOUVOGilbert
ConcordiaUniversity,Montreal,Canada
31. JUNJinWoo
InjeUniversity,Kimhae,RepublicofKorea
32. JUSHENKOEkaterina
TarasShevchenkoUniversity,Kyiv,Ukraine
33. KAROLAndrei
JointInstituteforNuclearResearch,Dubna,Russia
34. KHACHATRYANSuren
AmericanUniversityofArmenia,Yerevan,Armenia
35. KITLASAgnieszka
UniversityofBialystok,Poland
36. KLYACHKOAlexander
BilkentUniversity,Ankara,Turkey
37. KOSINARPeter
ComeniusUniversity,Bratislava,Slovakia
38. KOTECKYRoman
CharlesUniversity,PragueCzechRepublic&UniversityofWarwick,UK
39. KWONDoYong
KoreaInstituteforAdvancedStudy,Seoul,RepublicofKorea
40. LEFRANCMarc
UniversitédesSciencesetTechnologiesdeLille,France
41. LOEBLMartin
CharlesUniversity,Prague,CzechRepublic
42. LUQUEJean-Gabriel
UniversitédeMarne-La-Vallée,France
ix
43. MAKHLOUFAmar
UniversityofAnnaba,Algeria
44. METENSStéphane
UniversitéParis7-DenisDiderot,France
45. MOFFATTIain
CharlesUniversity,Prague,CzechRepublic
46. NESETRILJaroslav
CharlesUniversity,Prague,CzechRepublic
47. NOUVELBertrand
EcoleNormaleSupérieure,Lyon,France
48. OLSHEVSKIYAlexander
BryanskStateTechnicalUniversity,Russia
49. OPALKARoman
BazéracThézac,France
50. ORLEANDEAMarius-Ciprian
NationalInstituteofPhysicsandNuclearEngineering,Bucharest,Romania
51. PELANTOVAEdita
CzechTechnicalUniversity,Prague,CzechRepublic
52. POLISENSKAHana
CharlesUniversity,Prague,CzechRepublic
53. POPESCUBogdan
NationalInstituteofMaterialsPhysics,Bucharest,Romania
54. POPOVYCHStanislav
TarasShevchenkoUniversity,Kyiv,Ukraine
55. PROGULOVATatyana
SAMInternationalUniversityofNature,SocietyandMan,Dubna,Russia
56. ROVANBronislav
ComeniusUniversity,Bratislava,Slovakia
57. SAKAROVITCHJacques
Ecolenationalesupérieuredestélécommunications,Paris,France
58. SARGSYANLusine
AmericanUniversityofArmenia,Yerevan,Armenia
59. SHISHKOVANatalya
UkrainianNationalAcademyofSciences,Donetsk,Ukraine
60. SHMILOVICILEIBArmin
Ben-GurionUniversity,BeerSheva,Israel
61. SIMONNETPierre
UniversitédeCorse,Corte,France
62. SMOLINSKIKordian
UniversityofLodz,Poland
63. STEINERWolfgang
UniversitéParis7-DenisDiderot,France
64. SYCHDenis
M.V.LomonosovMoscowStateUniversity,Russia
65. THIBONJeanYves
UniversitédeMarne-La-Vallée,France