Generaldefinition
Italsoreferstothecharacteristicsofdifferentlevelscoexistinginthesamecupofcoffee.Thehighcomplexitymeansthattherearemoretypesofsensorystimulationthatcanbefelt;whatshouldbepaidattentiontoisthesefeelingsIncludingtheafter-rhyme,itisnotnecessarilylimitedtothepresentfeelingwhendrinking.
Algorithm
Complexity(computercomplexitytheory)
Computationalcomplexitytheory(Computationalcomplexitytheory)iscomputationaltheoryThefirstpartisabouttheresourcesneededtostudycomputingproblems,suchastimeandspace,andhowtosavetheseresourcesasmuchaspossible.
Themostcommonresourcesstudiedbycomputationalcomplexitytheoryaretimecomplexity(howmanystepsmustbetakentosolvetheproblem)andspacecomplexity(howmuchmemoryisneededtosolvetheproblem).Otherresourcescanalsobeconsidered,suchashowmanyparallelprocessorsareneededinparallelcomputingtosolvetheproblem.
Timecomplexityreferstothetimerequiredtocompleteanalgorithminthefieldofcomputerscienceandengineering,andisanimportantparametertomeasuretheprosandconsofanalgorithm.Thesmallerthetimecomplexity,thehighertheefficiencyofthealgorithm,andthemorevaluablethealgorithm.
Spacecomplexityreferstothestoragespacerequiredtocompleteanalgorithminthefieldofcomputerscience,whichisgenerallyafunctionofinputparameters.Itisanimportantmeasureoftheprosandconsofanalgorithm.Generallyspeaking,thesmallerthespacecomplexity,thebetterthealgorithm.WeassumethatthereisaTuringmachinetosolveacertainprobleminacertaintypeoflanguage.Xwordsbelongtothisproblem.PutXintotheinputofthisTuringmachine.ThisTuringmachineneedstosolvethisproblem.Thetotalnumberofgridsintheworkzoneiscalledspace.
Complexitytheoryisdifferentfromcomputabilitytheory.Thefocusofcomputabilitytheoryiswhethertheproblemcanbesolved,nomatterhowmanyresourcesareneeded.Asabranchofcomputationaltheory,complexitytheoryistosomeextentconsideredtobea"spear"and"shield"relationshipwithalgorithmtheory,thatis,algorithmtheoryfocusesondesigningeffectivealgorithms,whilecomplexitytheoryfocusesonunderstandingwhyForcertaintypesofproblems,thereisnoeffectivealgorithm.
Complexity(CPX):
TheconceptofcomplexitywasfirstproposedbyKolmgorov.Toputitsimply,thecomplexityofathingcanbemeasuredbythelengthofthecomputerlanguageusedtodescribeit.Itisgenerallybelievedthatthelongerthelengthofthecomputerlanguagedescribingathing,themorecomplexthething.Inthe1970s,Lempleetal.gaveadefinitiontothecomplexityofrandomsequencesintheresearchofinformationtheory.Theybelievedthatcomplexityreflectstherateatwhichnewpatternsappearinatimeseriesasitslengthincreases,andshowshowclosethesequenceistorandomness.Inthelate1980s,Kasperetal.studiedthecomplexityofrandomsequencesintheLem-Zivsense,andproposedspecificalgorithmsformeasuringthecomplexityofrandomsequences.ThecomplexitymeasureobtainedbythisalgorithmiscalledKccomplexity,anditispointedoutthatthisalgorithmissuperiortotheLyapunovexponent.Sincethecomplexityanalysismethoddoesnothavestrictrequirementsonthelengthofthesequence,itiswidelyusedinthefieldofsignalprocessing.
BeforecalculatingKc,thesequencetobeprocessedisfirstcoarse-grained,andtherandomsequenceisbinarizedhere,thatis,eachpointofthesequenceisrepresentedbyabit,soyoucanTheresearchedsignalinformationiscoarse-grainedtoforma"0,1"sequence.Assumingthatthetimetransmissionsequencetobeprocessedis{xi)(i=1,2,...,n),findtheaveragevalue.Ifxi≥averagevalue,setxi=1;ifxi
Kciscalculatedtofindthenumberofpatternscontainedinthesequencex,thespecificmethodistopassoneofthe“0,1”timeseriesAfterthestringofcharacterss(s1,s2,...,s.),addoneorastringofcharactersQtoseeifthecharacterQbelongstoSQv(SQvisobtainedbysubtractingthelastcharacterfromtheSQstring),ifitappearsThewordingofhasalreadybeenmentionedbefore,thatis,QisasubstringofsQ,thenthecharacteriscalled"copy".Itisconsideredthatthereisnonewpatterninthisprocess.Addthecharactertotheendofthestring,continuetoincreaseQ,andthenproceedJudgment;ifithasnotappearedbefore,then"insert"thischaracter,usea"·"toseparatethecharactersbeforeandafter"insert",andthinkthatanewpatternhasappeared:thenlookatallthecharactersbeforethelast"·"Tos,reconstructQ,repeattheaboveoperationuntiltheendofthesequenceandcalculatethesumofthenumberofpatternsfound.Forexample,thecomplexityofthesequence(0010)canbeobtainedbythefollowingsteps:
(1)Thefirstcharacterisalways0·;
(2)S=0,Q=0,SQ=00,SQv=0,QbelongstothesentenceSQv,0·0;
(3)s=0,Q=01,sQ=001,sQv=00,QdoesnotbelongtothesentencesQv,0·01·;
(4)S=001,Q=0,SQ=0010,SQv=001,QbelongstothewordSQv,0·01·0.
Sothenumberofpatternsinthesequenceis3,thatis,thecomplexityc(4)=3.Thesymbolsequence0000...shouldbethesimplest,0·000...,c(n)=2.Inaddition,suchas010101...shouldbe0.1.0101...,c(n)=3.
Asmentionedabove,thecharacterstringisdividedintosegmentswith"·".Thenumberofsegmentsisdefinedasthecomplexityc(n).Almostall"0,1"sequenceshavec(n)Tendtoafixedvalue,thatis:
limc(n)=b(n)=n/ln(n)
So,b(n)istheprogressivebehaviorofarandomsequence,Youcanuseittonormalizec(n)toarelativecomplexity:
C(n)=c(n)/b(n)
UsethisfunctionToexpressthecomplexchangesofthetimeseries,itcanbeseenthattheC(n)ofacompletelyrandomsequencetendsto1,whileotherregularandperiodicmotionstendto0,whilethec(n)ofanincompleterandomsequenceisbetweenthetwo.between.
Theprocessofcoarse-grainingisnotnecessarilylimitedtobinarization,andquaternization(SunHongetal.2002)orthemethodcalledfine-graining(ChenHongweiandChenYazhu,2004)canalsobeused.Thisresultismoreaccuratethanthecoarse-grainedcomplexity.