lindon shabd

ganitamadhye, sanyojanashastra aanee sanganak vidnyan yaa kshetranmadhye, lindon shabd haah eka rikt nasalela shabd aahe joou tyachya serve paribhramananpeksha shabdakosh kramvarit katekorpane lahan aahe. lindon shabdanna ganitshastradnya rogger lindon yanche naav denyat aale aahe, jyanni 1954 madhye tyancha shodh ghetala aanee tyanna manak shabdakosh anukram mhatale. anatoli shirshovne 1953 madhye lindon shabdanchi suruvat kelee, tyanna niyamit shabd mhatale. lindon shabd heey hallwardsche eka vishesh udaharan aahe; lindon shabdanche jawaljawal serve gunadharm hallwardsdware samayik kele jaatat.
vyakhya.
anek samatulya vyakhya astitvat aahet.
sootra 1-erii lindon shabd lambi sootra 2 haah aakar sootra 1 chya varnamalavaril sootra 3-varn string aahe aanee jeey tyachya serve paribhramananchya bahusanchatil shabdakosh kramatil adviteey kiman ghatak aahe. ekeri sarvat lahan paribhraman asane mhanje lindon shabd tyachya konatyahi kshullak firkipeksha vegala aahe aanee mhanoon too aperiodic aahe.
paryayane, sootra 5 haah shabd lindon shabd aahe, jarr aanee keval jarr too tyachya konatyahi yogya pratyayapeksha rikt nasel aanee shabdakoshdrushtya katekorpane lahan asel, tarr teey sootra 7 heey serve rikt nasalelya shabdansathi sootra 6 aahe, jase qee sootra 8 aanee sootra 9 rikt nastil.
aanakhi eka vaishishtya pudhilpramane aaheh lindon shabdacha gunadharm assa aahe qee too rikt nahee aanee jevha jevha too done rikt nasalelya substringmadhye vibhagala jaato, tevha dawa substering nehmi ujavya substringpeksha shabdakoshiyadrushtya qamee asato. mhanjech, jarr sootra 5 haah lindon shabd asel aanee sootra 8 heey done substringmadhye konatehi factorization asel, sootra 9 aanee sootra 7 heey rikame asalyache samajale tarr sootra 14. hii vyakhya soochit karate qee lambi sootra 16 chey string sootra 5 haah lindon shabd asel jarr aanee keval jarr lindon shabd formula 9 aanee formula 7 astitvat asateel tarr formula 14 aanee formula 8. jaree yaa gunadharmasah formula 9 aanee formula 7 chaa ekapeksha jaast paryay asoo shakato, taree eka vishisht paryay aahe, jyala "manak factorization" mhanatat, jyamadhye sootra 7 shakya titka lamb aahe.
ganana.
done-chinh dwaiti varnamalavaril lindon shabd, lambinusar kramvarit aanee nantar pratyek lambichya vargat shabdakoshatmakdrushtya, eka anant kram tayar karatat joou suru hoto.
yaa anukramashi sambandhit nasaleli pahili string, '00' vagalali jaate kaaran tee niyatkalik aahe (tyat '0' yaa substringchya done punaravrutti asatat); dusari vagalaleli string, '10', aperiodic aahe parantu tyachya kramparivartan vargat kiman nahee kaaran tee lahan string '01' varr chakriyapane krambaddha kelee jaau shakate.
rikami string shoonyachya lambichya lindon shabdachya vyakhyeshi dekhil julate. pratyek lambichya dwaiti lindon shabdanchya sankhya, shunyapasoon suru houn, purnank kram tayar karatat.
lindon shabd aperiodic haar varg pratinidhinshi sambandhit aahet aanee asha prakare morochya haar-mojanichya karyasah mojale jaau shakatat.
pidhi.
 shabdakosh kramvarit dilelya varnamala aakar sutrasah jastit jaast sootra _ 3 varr lambichya lindon shabdanchi yadee karnyasathi eka karyaksham algoridam pradan karate. jarr sootra 5 haah kramatil shabdanpaiki eka asel, tarr sootra 5 nantarcha shabd khaleel khaleel shodhala jaau shakatoh
yaa prakriyedvare sootra _ 5 yaa shabdacha uttaradhikari tayar karnyasathi sarvat white vel mhanje sootra _ 39.
tathapi, jarr tayar kele jaanare shabd lambichya sootra _ 3 chya rachnet sathavale gele asateel aanee sootra _ 5 madheel sootra _ 29 chey bandhkam sootra _ 5 chee naveen prat banavanyaivaji sootra _ 5 chya shevati chinhe jodoon kele gele asel, tarr sootra _ 5 chaa uttaradhikari tayar karnyasathi sarasari vel sthir aahe (pratyek shabd titkach sambhavya aahe asey gruheet dharoon). mhanoon, jastit jaast sootra _ 3 vareel lambichya serve lindon shabdancha kram anukramachya lambichya pramanat velet tayar keela jaau shakato. yaa kramatil shabdanchya sthir apurnankachi lambi achook sootra _ 3 asate, mhanoon tyach prakriyecha vapar yaa nikashanshi julat nasalelya vyutpann shabdanna galoon, achook sootra _ 3 kinwa jyaa shabdanchi lambi sootra _ 3 vibhajit karate asha shabdanchya lambiche shabd karyakshamatene tayar karnyasathi keela jaau shakato.
manak gunank.
cheen-fox-lindon prameyanusar, pratyek string lindon shabdanchya kramane asha prakare ekatra karoon adviteey paddhatine tayar kelee jaau shakate qee kramanusar shabd shabdakoshdrushtya vadhat naheet. yaa kramatil antim lindon shabd haah dilelya stringcha shabdakoshshastriyadrushtya sarvat lahan pratyay aahe. lindon shabdanchya vadhatya kramane (tathakathit lindon factorization) factorization resheey velet tayar kele jaau shakate. lindon factorization vapar deta compressionsathi aanee digital bhoomitisathi algoridammadhe buro-wheeler transformchya bijective prakaracha bhag mhanoon keela jaau shakato.
asha gunankanamadhye (advitiyapane) varnamaladvare label kelelya panansah, antim lindon shabdane dilelya pratyek ujavya bajuchya shakhesah, maryadit dwaiti vruksh mhanoon lihile jaau shakate.
asha zadanna kadhikadhi manak bandhane mhanatat aanee mukt gatachya ghatakanche gunank mhanoon kinwa mukt khote bijganitache aadhar ghatak mhanoon ghetale jaau shakatat. hii zaade dalan vrukshanche eka vishesh udaharan aahet (lindon shabd heey dalan shabdanche eka vishesh udaharan aahe) aanee tyachpramane, dalan shabd eka manak kram pradan karatat, jyala gatansathi commutator sankalan prakriya mhanatat aanee khote algebracha aadhar aahe.
kharey tarr, teey sarvatrik aachchadan algebranchya bandhkamasathi aavashyak asalelya poinker-berkhoff-viit prameyat prameyat commutatorsathi eka spasht rachana pradan karatat.
pratyek lindon shabd kramparivartan mhanoon samajala jaau shakato, pratyay manak kramparivartan.
duval algoridam.
 resheey vel aanee sthir jaaget chalanare manak ghatak shodhanyasathi eka algoridam vikasit kele. shakya titka lamb lindon shabd shodhanyacha prayatna vibhajit stringvar teey punaravrutti karate. jevha tyala eka sapadato, tevha too tyala parinamanchya yadeet jodato aanee stringcha urvarit bhag shodhanyasathi pudhe jaato. stringchi parinami yadee hii dilelya stringche manak gunankan aahe. algoridamche adhik aupcharik varnan khalilpramane aahe.
aine' lambichi 'ess' string dilyas, khaleel khaleel pudhe jaaveh
dii bruision sequenceshy jodani.
jarr konee shabdakoshachya kramane, dilelya sankhya "aine" laa vibhajit vibhajit lambiche serve lindon shabd ekatra jodale, tarr parinam dii bruision kram aahe, chinhancha eka golakar kram aahe, jase qee pratyek sambhavya lambi-"aine" kram tyachya sanlagn anukramanpaiki eka mhanoon agadi ekada disato. udaharanarth, dviaadhari lindon shabdanche sanyojan, jyachi lambi chaar bhagate,
hii rachana, lindon shabdanchya karyaksham nirmitisah, resheey vel aanee laghuganak jaaget vishisht dii bruision kram tayar karnyasathi eka karyaksham paddhat pradan karate.
atirikt gunadharm aanee anuprayog.
dilelya padvichya eksandh bhagasathi aadhar tayar karnyasathi, mukt khote algebranchya varnanasathi lindon shabdancha vapar hoto; yaa shabdancha parichay karoon denyasathi lindonchi hii mool prerana hotee. lindon shabd heey sabhagruh sanchanche eka vishesh prakaran mhanoon samajale jaau shakatat.
mukhya "pii" sathee, kshetra sootra _ 50 varr "dii" degreechya irreducible monic bahupadichi sankhya hii "pii" chinhanchya varnamalemadhye "dii" lambichya lindon shabdanchya sankhyeitakich aahe; teey spasht patravyavaharat thewale jaau shakatat.
radfordche eka pramey asey sangate qee 0 yaa vaishishtyapurn kshetravaril ferbadal bijganitakade lindon shabdanvar bahupadi bijganit mhanoon pahile jaau shakate. adhik tantotant, 'aaa' heey varnamala asoo dya, 'keey' heey vaishishtyapurn 0 chey kshetra asoo dya (kinwa, adhik samanya, eka parivartanatmak sootra _ 51-bijganit), aanee 'aar' heey mukt gair-vinimayatmak 'keey'-bijganit asoo dya. tyanantar 'aaa' vareel shabdanna 'gair-vinimayatmak ekshabd' (i.eae., 'xa' chee utpadane) 'r' madhye; mhanje, aapan eka shabd olakhato ('a' 1, 'a' 2..," a ") ekmudra" x "a" 1 "x" a "2 saha.."zanne". asha prakare, "aaa" vareel shabd "aar" chaa "keey"-vector space besis tayar karatat. mug, 'aar' varr 'shuffle utpadan' paribhashit kele jaate; heey eka 'keey'-dvimiteey, sahyogi aanee parivartaneey utpadan aahe, jeey shh dware darshavile jaate aanee jyaa shabdanvar punaravruttidvare paribhashit kele jaau shakate
aaa" varnamalavaril "ferbadal bijganit" hii gunakar mhanoon shsah sampann 'aar' haah yogatmak gut mhanoon paribhashit kelee jaate. radfordche pramey aata asey sangate qee lindon shabd heey yaa ferbadal bijganitache bijganitiyadrushtya swatantra ghatak aahet aanee teey tayar karatat; asha prakare, ferbadal bijganit heey lindon shabdanshi sambandhit anishchitansah, "keey" vareel bahupadi ringsathi samaroop aahe.

