關于有限自動機的Hankel行列式序列及其復雜性.pdf

1、華中科技大學碩士學位論文關于有限自動機的Hankel行列式序列及其復雜性姓名：薛靜申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：文志雄20110525AbstractThisthesisstudiessomepropertiesoftheHankeldeterminantsequenceoffiniteautomatonitscomplexity.ThueMsesequenceastheearliestoccuringautomaticse

2、quencehasbeeninitiatedbyThuewhoproveditdoesnotcontainthreeconsecutiveidenticalblocks.AfewyearslaterMsestudiedthetopologicaldynamicalsystemwhichisgeneratedbythissequenceGottschalkstudiedthissequenceintheframewkofminimalse

3、ts.Sincethe60soflastcenturypeoplefoundmanyimptantinterestingpropertiesofthissequencetimeagainfromdifferentfields.Becauseofitssimplestructurepeopleoftenuseitasthetouchstoneofautomaticsequence.Inthelasttwentyyearsitoccured

4、inmanydifferentfieldsofmathematicssuchas:finiteautomatatheyfmallanguagetheyergodictheynumbertheyalgebraicfmalseriesoverGF2(X)alsoinphysicsinrelationtoquasicrystals.ThepropertiesofHankeldeterminantsassotiatedwithasequence

5、arecloselyconnectedtothestudyofthemomentproblemtoPadeapproximationtocombinatialpropertiesofthesequence.ThisthesisdiscussessomenewpropertiesofThueMsesequence.Themainwkofthisthesisisthedeductionoffundamentalreccurenceequat

6、ionsoftheHankeldeterminantsequenceofThueMsesequenceperioddoublingsequencetheproofoftheperiodicautomaticitypropertyofthesesequencethecomputationoftheirlowcomplexity.Inthepreparationsectionweintroducethedefinitionsproperti

7、esofthesubstitutionsequencefiniteautomaticsequenceThueMsesequencesomelemmasrelatedwithmatricesoperation.WededuceprovesixteenfundamentalrecurrenceequantionsofHankeldeterminantsequenceofThueMsesequenceperioddoublingsequenc

8、einthethirdchapterdiscusstheperiodicautomaticitypropertiesofthesesequences.Finallyrelatedapplicationspopulizationsaregivenfromthepointofviewofgeneratingseries(strong)nonrepetitivestructureofsequencePadeapproximationlowco