
aspashtamaina upa beejaganitam

aspashtamaina upa algibras siddhaantam anedi aspashtamaina samiti siddhaantam yokka oka adhyayam. idhi saadhaaranamgaa icchina beejaganita nirmaanam yokka upa beejaganitam yokka bhavananu vyaktam chese suutraala yokka bahula-viluva tarkamlo oka vivarana nundi pondabadutundi.
nirvachanam.
monadic predicate chihnamtho beejaganita nirmaanaala kosam modati arder bhashanu pariganinchandi. appudu "aspashtamaina upa beejaganitam" anedi edainaa "n"-ary operation h kosam, suutraalanu kaligi unna siddhaantam yokka aspashtamaina namuunaa.
suutram _ 1
mariyu, edainaa sthiraamkam c, s (c) kosam.
modati suutram operation h kii sambandhinchi s yokka moosivetanu vyaktam chestundi, mariyu rendavadi c anedi s looni oka moolakam anae vaastavaanni vyaktam chestundi. udaaharanaku, madimpu nirmaanam [0,1] loe nirvachinchabadindani mariyu samyogaanni ardham chesukovadaniki upayoginche [0,1] loe operation suutram _ 2 dwara soochinchabadutundani anukundam. appudu oka beejaganita nirmaanam yokka aspashtamaina upa beejaganitam, dheeni domine d, prati d1 kii, d yokka aspashtamaina upasamiti dwara nirvachinchabadutundi.., dn loe d, h anedi n-aari operation chihnam h yokka vivarana ayithe, appudu
antekakunda, c anedi sthiraamkam c yokka vivarana ayithe, adhi s (c) = 1.
ekkuvagaa adhyayanam cheyabadina aspashtamaina upa algibras yokka taragati, dheenilo operation formula _ 2 kaneesamtho samanamga untundi. atuvanti sandarbhamlo eee krindi pratipaadananu niroopinchadam takshaname.
pratipaadana. [0,1] looni prati λ kii, s yokka closed cutt {x ωd: s (x) ωλ} anedi sub algibra ayithe matrame beejaganita nirmaanam yokka aspashta upasamiti s anedi aspashtamaina sub algibra nii nirvachistundi.
aspashtamaina upa samuuhaalu mariyu upamaanaayidlu.
aspashtamaina upa samuuhaalu mariyu aspashtamaina upamaanavaayuvulu mukhyamgaa aspashtamaina upulgibras yokka aasaktikaramaina taragatulu. atuvanti sandarbhamlo monoid (m, β, u) yokka aspashtamaina upasamiti "s" anedi aspashtamaina upamanamga untundi, ayithe mariyu unte matrame
ikkada a loe tatastha moolakam u.
oka samuuham g ichinatlayithe, g yokka aspashtamaina upa samuuham g yokka aspashtamaina upamanavayuvu s. 
aspashtamaina upa samuuham yokka bhavana aspashtamaina samaanatvam yokka bhaavanalatho khachitamgaa sambandham kaligi undani niroopinchadam saadhyamavutundi. vaastavaaniki, s anedi oka samiti, g anedi s looni parivartanala samuuham mariyu (g, s) anedi g yokka aspashtamaina upa samuuham anie anukundam. appudu, amarchadam dwara 
manam aspashtamaina samaanatvaanni pondutaamu. dheeniki viruddhamgaa, e anedi s loe aspashtamaina samaanatvam mariyu, s yokka prati parivartanaku, sett cheyandi 
appudu s anedi s loe parivartana yokka aspashtamaina upasamuuhaanni nirvachistundi. idhe vidhamgaa manam aspashtamaina submonoidlanu aspashtamaina aardarlatho anusandhaaninchavacchu.

