Automata, Universality, Computation: Tribute to Maurice Margenstern

421 Pages·2015·16.765 MB·English

by  Andrew Adamatzky (eds.)

Emergence, Complexity and Computation ECC
Andrew Adamatzky Editor
Automata,
Universality,
Computation
Tribute to Maurice Margenstern
Emergence, Complexity and Computation
Volume 12
Serieseditors
IvanZelinka,TechnicalUniversityofOstrava,Ostrava,CzechRepublic
e-mail:[email protected]
AndrewAdamatzky,UniversityoftheWestofEngland,Bristol,UnitedKingdom
e-mail:[email protected]
GuanrongChen,CityUniversityofHongKong,HongKong
e-mail:[email protected]
EditorialBoard
AjithAbraham,MirLabs,USA
AnaLuciaC.Bazzan,UniversidadeFederaldoRioGrandedoSul,PortoAlegre
RSBrasil
JuanC.Burguillo,UniversityofVigo,Spain
SergejCˇelikovský,AcademyofSciencesoftheCzechRepublic,CzechRepublic
MohammedChadli,UniversityofJulesVerne,France
EmilioCorchado,UniversityofSalamanca,Spain
DonaldDavendra,TechnicalUniversityofOstrava,CzechRepublic
AndrewIlachinski,CenterforNavalAnalyses,USA
JouniLampinen,UniversityofVaasa,Finland
MartinMiddendorf,UniversityofLeipzig,Germany
EdwardOtt,UniversityofMaryland,USA
LinqiangPan,HuazhongUniversityofScienceandTechnology,Wuhan,China
GheorghePa˘un,RomanianAcademy,Bucharest,Romania
HendrikRichter,HTWKLeipzigUniversityofAppliedSciences,Germany
JuanA.Rodriguez-Aguilar,IIIA-CSIC,Spain
OttoRössler,InstituteofPhysicalandTheoreticalChemistry,Tübingen,Germany
VaclavSnasel,TechnicalUniversityofOstrava,CzechRepublic
IvoVondrák,TechnicalUniversityofOstrava,CzechRepublic
HectorZenil,KarolinskaInstitute,Sweden
AboutthisSeries
The Emergence,Complexityand Computation(ECC) series publishesnew devel-
opments,advancementsandselectedtopicsinthefieldsofcomplexity,computation
andemergence.Theseriesfocusesonallaspectsofreality-basedcomputationap-
proachesfromaninterdisciplinarypointofviewespeciallyfromappliedsciences,
biology, physics, or Chemistry. It presents new ideas and interdisciplinary insight
onthe mutualintersectionofsubareasofcomputation,complexityandemergence
anditsimpactandlimitstoanycomputingbasedonphysicallimits(thermodynamic
and quantumlimits, Bremermann’slimit, Seth Lloyd limits...) as well as algorith-
mic limits (Gödel’s proof and its impact on calculation, algorithmic complexity,
theChaitin’sOmeganumberandKolmogorovcomplexity,non-traditionalcalcula-
tionslike Turingmachineprocessand its consequences,...)and limitationsarising
inartificialintelligencefield.Thetopicsare(butnotlimitedto)membranecomput-
ing,DNAcomputing,immunecomputing,quantumcomputing,swarmcomputing,
analogic computing,chaos computingand computingon the edge of chaos, com-
putationalaspectsofdynamicsofcomplexsystems(systemswithself-organization,
multiagentsystems,cellularautomata,artificiallife,...),emergenceofcomplexsys-
temsanditscomputationalaspects,andagentbasedcomputation.Themainaimof
thisseries itto discussthe abovementionedtopicsfroman interdisciplinarypoint
ofviewandpresentnewideascomingfrommutualintersectionofclassicalaswell
asmodernmethodsofcomputation.Withinthescopeoftheseriesaremonographs,
lecture notes, selected contributionsfrom specialized conferencesand workshops,
specialcontributionfrominternationalexperts.
Moreinformationaboutthisseriesathttp://www.springer.com/series/10624
Andrew Adamatzky
Editor
Automata, Universality,
Computation
Tribute to Maurice Margenstern
ABC
Editor
AndrewAdamatzky
UnconventionalComputingCentre
UniversityoftheWestofEngland
Bristol
UnitedKingdom
ISSN2194-7287 ISSN2194-7295 (electronic)
Emergence,ComplexityandComputation
ISBN978-3-319-09038-2 ISBN978-3-319-09039-9 (eBook)
DOI10.1007/978-3-319-09039-9
LibraryofCongressControlNumber:2014945747
SpringerChamHeidelbergNewYorkDordrechtLondon
(cid:2)c SpringerInternationalPublishingSwitzerland2015
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
[SpringerInternationalPublishingAGSwitzerland]ispartofSpringerScience+BusinessMedia
(www.springer.com)
Preface
A Tribute to MauriceMargenstern
A few figures witness Maurice Margenstern’s scientific accomplishments. He au-
thored or co-authored 210 papers (some more being on the way...). His 54
co-authors are from all over the world: France, Belgium, Switzerland, Germany,
Austria,Italy,Spain,Ireland,UnitedKingdom,Finland,Hungary,Moldavia,Roma-
nia,Russia,Israel,China,Malaysia,Japan,Chili,USA.Besideshisresearchpapers,
he wrote 6 books, organizedand edited the proceedingsof 8 internationalconfer-
ences,supervised5students.
And,mostimportantly,hepioneerednewareasofresearchattheintersectionof
mathematicsandcomputerscience.
HowdidMauricebecomethescientistwesomuchappreciate?
Maurice was bornin Parison June 6, 1947.After highschoolhe was accepted
in prestigious French “grandes e´coles”. Resigning from the E´cole Polytechnique
he entered the E´cole Normale Supe´rieure de Cachan. After he passed the French
“agre´gation de mathe´matiques”, he got an academic position at the mathematics
departmentoftheUniversityofParis-Sud(Orsay)in1970.
Attractedbyconstructivemathematics,thenaverymarginalsubjectinFrance,he
wentintheearly70’stoLeningradtostudywithNicola¨ıA.Shanin,thentheheadof
the famousRussian schoolin constructivemathematicsfoundedby A.A. Markov.
This is where he worked on his thesis on Constructive topological properties of
spacesofalmostperiodicfunctions.
Thenhisscientificinclinationsgraduallymovedfromconstructivemathematics
tocomputability,asubjectthenmuchrevivedafterMatijasevich’sfamousresulton
Hilbert’s 10thproblem.In the late 80’s he joined the computerscience laboratory
LITP (now LIAFA) in Paris and started his amazing investigation of the simplest
(resp.mostcomplex)machineswithanundecidable(resp.decidable)haltingprob-
lem.DespitethepreviousworksbyYuriRogogineinMoldaviaandLudmilaPavlot-
skaia in Russia, this topic was then rather confidential. Maurice is to be credited
forputtingitupasoneoftheimportantthemesincomputability.Hedidsoviahis
VI Preface
owncontributionsandviaatriennialinternationalconferenceMachines,Computa-
tionsandUniversality hesetupin 1995andwhichstill goeson.Irememberhow
Josef Gruska (speaking as the last chairman of the first conference,held in Paris)
stressedhowmuchenergyMauricehadtoshowinordertocreatefromscratchsuch
asuccessfulinternationalevent.
MauricepassedhisHabilitationin1994“Studyofthefrontierbetweendecidabil-
ity and undecidability of the halting problem of small or constrained Turing ma-
chines.”Hewasthenappointedasaprofessorincomputersciencebytheuniversity
ofLorraineatMetz.TherehecreatedtheLITAlaboratoryandspentmuchenergy
tomakeitasolidresearchcenter.Someyearsago,hewaspromoted“professeurde
classeexceptionnelle”,thehighestrankinFrenchAcademia.
In the early 2000’s Maurice developed the subject of computation with cellu-
lar automata in the hyperbolic world (dimension 2, 3 or 4) and broughtsolutions
tolongopendifficulttilingproblems.Besidesthese technicalachievements,Mau-
rice provedthathyperboliccomputabilityallowsto overcomeknownunfeasibility
resultsoftheEuclideanworld.
The classical tool in hyperbolic geometry is the theory of groups but Maurice
invented completely new tools: combinatorial ones. As is usual with new ideas,
expertsin hyperbolicgeometryshowed reluctancetowardssuch an innovativeap-
proach and it was a real relief for Maurice when Donald Knuth wrote to him to
expressthathefoundthese newtools“quitefascinating”andwillrefertothemin
theArtofComputerProgramming.
Ofcourse,thetwothemespresentedabovedonotexhaustthesubjectsMaurice
investigatedbuttheywitnesshiscreativetalentandimpressiveenergy.
MauricerecentlyretiredandisnowemeritusprofessorattheuniversityofLor-
raine.Havingnomoretoteachandmanagearesearchteam,Mauricesimplyspends
moretimetocontinueproducingprominentworks.
Having had the privilege to know him since the mid 70’s, it is my pleasure to
say,inthenameofallcontributorsofthisvolume:Maurice,thankyouforwhatyou
haveaccomplishedandlet’scontinueourfriendshipandscientificcollaboration.
SergeGrigorieff
Paris
Contents
1 TheCommonStructureoftheCurvesHaving
aSameGaussWord ........................................... 1
BrunoCourcelle
1.1 Introduction............................................. 1
1.2 Definitions.............................................. 4
1.3 AtomsofGraphsandMaps................................ 10
1.4 Planart-Graphsandt-Maps................................ 17
1.5 CurvesinthePlane....................................... 20
1.6 SomeOpenQuestions .................................... 35
References.................................................... 36
Appendix..................................................... 37
2 LogicalTheoryoftheAdditiveMonoidofSubsetsofNatural
Integers...................................................... 39
ChristianChoffrut,SergeGrigorieff
2.1 Introduction............................................. 39
2.2 Preliminaries............................................ 41
2.3 UsingSubmonoidstoApproximateandEmulate .............. 48
2.4 ComplexityoftheTheory ................................. 58
2.5 NonDefinablePredicates.................................. 60
2.6 LogicalDefinabilityin(cid:2)P(N);+,=(cid:3) ........................ 68
2.7 RemarkableDefinableSetsandClasses...................... 69
2.8 Conclusion.............................................. 73
References.................................................... 73
3 SomeReflectionsonMathematicsandItsRelationtoComputer
Science....................................................... 75
LiesbethDeMol
3.1 MathematicalLogic,theComputerandMathematics .......... 76
3.2 ANumber-Theorist’sPointofView......................... 80
VIII Contents
3.3 The Impact of the Computer on Mathematics: Some
QuantitativeResults ...................................... 83
3.4 Computer-AssistedExplorativeMathematics:Characteristics
andProblems............................................ 86
3.5 Some(NewandOpen)Problems ........................... 90
3.6 SomeAfterthoughts ...................................... 98
References.................................................... 99
4 SamplingaTwo-WayFiniteAutomaton ......................... 103
ZheDang,OscarH.Ibarra,QinLi
4.1 IntroductionandMotivation ............................... 103
4.2 InformationDependencyandInformationFlowin2NFAs ...... 105
4.3 LanguagePropertiesofSampledRunsofSomeTwo-Way
Infinite-StateAutomata ................................... 112
4.4 Conclusions............................................. 114
References.................................................... 114
5 Maurice Margenstern’sContributionsto the Field ofSmall
UniversalTuringMachines..................................... 117
TurloughNeary,DamienWoods
5.1 Introduction............................................. 117
5.2 SimulatingtheCollatzFunctionwithSmallTuringMachines ... 118
5.3 FrontiersbetweenUniversalityandNon-universality........... 120
5.4 RestrictedTuringMachines................................ 121
References.................................................... 124
6 ConstructingReversibleTuringMachinesbyReversibleLogic
ElementwithMemory......................................... 127
KenichiMorita
6.1 Introduction............................................. 127
6.2 ReversibleLogicElementwithMemory(RLEM) ............. 128
6.3 RelationtoPhysicalReversibility........................... 130
6.4 ConstructingReversibleTuringMachinesbyRotaryElement ... 132
6.5 ConcludingRemarks ..................................... 137
References.................................................... 137
7 TheGrossoneMethodologyPerspectiveonTuringMachines....... 139
YaroslavD.Sergeyev,AlfredoGarro
7.1 Introduction............................................. 139
7.2 TuringMachines......................................... 141
7.3 TheGrossoneLanguageandMethodology ................... 147
7.4 ObservingTuringMachinesthroughtheLensoftheGrossone
Methodology............................................ 153
7.5 ConcludingRemarks ..................................... 165
References.................................................... 167
Contents IX
8 OnParallelArrayPSystems ................................... 171
LinqiangPan,GheorghePa˘un
8.1 Introduction............................................. 171
8.2 DefinitionsandNotations ................................. 172
8.3 ParallelArrayPSystems .................................. 173
8.4 Results ................................................. 175
8.5 ConcludingRemarks ..................................... 180
References.................................................... 181
9 SmallPSystemsDefiningNon-semilinearSets.................... 183
ArtiomAlhazov,RudolfFreund
9.1 Introduction............................................. 183
9.2 Definitions.............................................. 185
9.3 AcceptingPSystems ..................................... 193
9.4 GeneratingbyDoublingintheMaximallyParallelMode ....... 195
9.5 AsynchronousandSequentialPsystems ..................... 202
9.6 PSystemswithCatalysts.................................. 203
9.7 Conclusions............................................. 215
References.................................................... 216
10 GeneralizedCommunicatingPAutomata........................ 219
Erzse´betCsuhaj-Varju´,Gyo¨rgyVaszil
10.1 Introduction............................................. 219
10.2 PreliminariesandDefinitions .............................. 220
10.3 ThePowerofPAutomatawithGeneralizedCommunication.... 226
10.4 Conclusions............................................. 235
References.................................................... 235
11 ComputationalModelsBasedonSplicing ........................ 237
YuriiRogozhin,SergeyVerlan
11.1 Introduction............................................. 237
11.2 SplicingOperationandHSystems .......................... 238
11.3 ControlledSplicing....................................... 241
11.4 DistributedSplicing ...................................... 248
11.5 RefiningtheControl...................................... 253
11.6 Conclusions............................................. 255
References.................................................... 256
12 LinearCellularAutomataandDecidability ...................... 259
KlausSutner
12.1 LinearCellularAutomata ................................. 259
12.2 TheFirst-OrderTheory ................................... 262
12.3 UndecidabilityandHardness............................... 269
12.4 Summary ............................................... 273
References.................................................... 274