
uchita booliyan beejaganitam

ganita saastramlo, uchita booliyan beejaganitam anedi oka booliyan beejaganitam, idhi generatorlu anie piluvabade pratyaekamaina muulakaala samititoe untundi, avih
oka saadhaarana udaaharana.
uchita booliyan beejaganitam yokka generatorlu swatantra pratipaadanalanu suuchimchagalavu. udaaharanaku, "zaan podavainavadu" mariyu "maerii dhanavanthudu" anae pratipaadanalanu pariganinchandi. ivi naalugu anuvulatho kuudina booliyan beejaganitaanni utpatti chestaayi, avih
booliyan beejaganitamloni itara muulakaalu anuvula taarkika vibhajanalu, "zaan podavainavadu mariyu maerii dhanavanthudu kaadu, ledhaa zaan podavu kaadu mariyu maerii dhanavanthudu". adanamgaa maroe moolakam undhi, tappu, dheenini khaalii vibhajanaga bhaavinchavachchu; antey, anuvula vibhajana kaadu.
eee udaaharana 16 muulakaalatoe kuudina booliyan beejaganitaanni istundi; saadhaaranamgaa, parimita "n" kosam, "n" generatorlatho kuudina uchita booliyan beejaganitamlo 2 "n" anuvulu untaayi, anduvalla suutram _ 1 muulakaalu untaayi.
anantamaina generatorlu unte, ippudu anuvulu levani tappa idhe paristhiti untundi. booliyan beejaganitamloni prati moolakam anedi utpatti chese aneka pratipaadanala kalayika, avi taarkikamgaa samanamga unte alanti rendu muulakaalu okela pariganinchabadataayi.
n-moolakam samitilooni uchita booliyan beejaganitam suutram _ 1 muulakaalanu enduku kaligi undho chuudataaniki maroka maargam emitante, prati moolakam n bits nundi okadaaniki function anie gamaninchadam. atuvanti functionku suutram _ 3 saadhyamayye inputlu unnaayi mariyu function prati inputku avtput cheyadaaniki 0 ledhaa 1nii enchukuntundi, kabatti suutram _ 1 saadhyamayye vidhulu unnaayi.
vargam-siddhaantaparamaina nirvachanam.
varga siddhaantam yokka bhaashalo, uchita booliyan algibralanu kevalam samuuhaalu mariyu vidhula vargam, samiti mariyu booliyan algibralu mariyu booliyan beejaganitam homomorphisms, baa madhya anubandham paramgaa nirvachinchavacchu. vaastavaaniki, eee vidhanam saarvatrika beejaganitam yokka chatramlo nirvachinchadagina edainaa beejaganita nirmaanaaniki saadhaaraneekaristundi.
paina, uchita booliyan beejaganitam anedi oka nirdishta maargamlo pravartinche generatorla samititoe kuudina booliyan beejaganitam anie memu cheppamu; pratyamnaayamgaa, okaru oka samititoe praarambhinchi, adhi yea beejaganitamnu utpatti chestundo adagavacchu. prati samiti "x" anedi beejaganitam anie nirvachinchabadina uchita booliyan beejaganitam "fx" nuu utpatti chestundi, prati beejaganitam "b" mariyu function "f": "x" "b" kii, oka pratyaekamaina booliyan beejaganitam homomorphism "f": "fx" "b" untundi, idhi "f" nii vistaristundi. rekhaachitramgaa,
ikkada "i" "x" anedi cherika, mariyu dyaash chesina baanam pratyaekatanu suuchistumdi. aalochana emitante, "x" yokka muulakaalanu ekkada pampaalo enchukunna tarvaata, booliyan beejaganitam homomorphisms yokka chattalu uchita beejaganitam "fx" loe migatavanni ekkada pampaalo nirnayistaayi. fx" loe "x" yokka muulakaala kalayikaga varninchaleni muulakaalu unte, appudu "f" "pratyekamainadi kaadu, mariyu" x "yokka muulakaalu taginanta swatantramgaa lekapothe, appudu" f "" baga nirvachinchabadadu! fx" pratyekamainadi (isomorphism varaku) anie sulabhamgaa choopabadutundi, kabatti eee nirvachanam ardhame. modata nirvachinchinatlugaa, x samitini utpatti chese uchita booliyan beejaganitam "fx" kuu isomorphic anie kooda sulabhamgaa choopabadutundi, kabatti rendu nirvachanalu angeekaristaayi.
paina perkonna nirvachanam yokka oka lopam emitante, rekhaachitram "f" anedi homomorphism anie sangrahinchadu; idhi samitilooni rekhaachitram kabatti prati baanam kevalam oka functionnu suuchistumdi. dheenini rendu rekhachitraluga vibhajinchadam dwara manam dheenini parishkarinchavacchu, okati baa loe mariyu okati sett loe. rendintinee anusandhaaninchadaaniki, beejaganita nirmaanaanni "marachipoye" functor "u": baa → setnu parichayam chestaamu, algibralu mariyu homomorphismlanu vaati antarleena setlu mariyu functionlaku mapping chestaamu.
paie baanaanni baa looni rekhaachitramgaa mariyu diguva tribhujaanni samitilooni rekhaachitramgaa ardham chesukunte, appudu eee rekhaachitram prati function "f": "x" "" ub "oka pratyaekamaina booliyan beejaganitam homomorphism" f ":" fx "" "b" kuu vistarinchindani sarigga vyaktam chestundi. functor "yuu" nuu homomorphism "eff" nuu tirigi setloki laagadaaniki oka parikaramgaa bhaavinchavachchu, tadwara idhi "eff" kuu sambandhinchinadi kaavacchu.
dheeni yokka visaeshamaina amsam emitante, rendu functorlu pakkane unnappudu vividha (samaanamaina) nirvachanaalalo rendo rekhaachitram okati. mana "f" sulabhamgaa functor sett → baa varaku vistaristundi, mariyu uchita booliyan beejaganitam "fx" nuu utpatti chese "x" yokka mana nirvachanam khachitamgaa "u" kii edama prakkane "f" untundi.
sthalavignaana saakshaatkaaram.
κ generatorlatho kuudina uchita booliyan beejaganitam, ikkada κ anedi parimita ledhaa anantamaina cardinal sankhya, {0,1} κ yokka anni clopen upasamitula sekaranagaa grahinchavacchu, utpatti topologyni batti, {0,1} vivikta topologyni kaligi undani bhaavistaaru. prati α <κ kii, α "va" generator anedi {0,1} κ yokka anni muulakaala samiti, dheeni α "va" coordinate 1. mukhyamgaa, suutram _ 5 generatorlatho kuudina uchita booliyan beejaganitam anedi cantor space yokka anni clopen upasamitula sekarana, konnisaarlu dheenini contor beejaganitam anie pilustaaru. eee sekarana lekkinchadaginadi. vaastavaaniki, "n" generatorlu ", n" parimitamaina uchita booliyan beejaganitam cardinality suutram _ 1 kaligi undagaa, suutram _ 5 generatorlatho kuudina uchita booliyan beejaganitam, suutram _ 5 generatorlu mariyu lekkinchadagina aneka parimita kaaryakalaapaalato kuudina edainaa uchita beejaganitam kosam, cardinality suutram _ 5 kaligi untundi.
uchita booliyan beejaganitaaniki eee sthalavignaana vidhanam gurinchi marinta telusukovadaaniki, booliyan algibras kosam stone yokka praatinidhya siddhaantaanni chudandi.

