
surjunctive group

ganita saastramlo, surjunctive group anedi oka samuuham, prati injective cellular automaton daani kanaalugaa samuuha muulakaalatoe kooda surjectivega untundi. surjunctive groupulu pravesapettabaddaayi. prati samuuham surjunctive avtundo ledho teliyadu.
nirvachanam.
cellular automaton anedi kanaala yokka kramabaddhamaina vyavasthanu kaligi untundi, prati okkati parimita varnamaala nundi oka chihnanni kaligi untundi, porugu kanaala viluvala aadhaaramgaa anni kanaalanu ekakaalamlo naveekarinchadaaniki "transition function" anie piluvabade ekareeti niyamanni kaligi untundi. chaalaa saadhaaranamgaa kanaalu oka rekha ledhaa adhika-dimensional puurnaanka grid roopamlo amarchabadi untaayi, conny kanaala itara amarikalu kooda saadhyame. kanaalaku avasaramainadi emitante, avi prati kanam "prati itara kanam vale kanipinche" nirmaanaanni yerparustaayih kanaala amarika mariyu edainaa kanaanni yea itara kanaanikainaa teesukelle niyama samiti rendinti samaruupata untundi. ganitasaastraparamgaa, dheenini oka samuuham anae bhavana dwara lanchanaprayamga cheyavachu, idhi anubandha mariyu viloma binary operation thoo kalisi muulakaala samiti. samuuhamlooni muulakaalanu samuuha karyakalapala dwara utpatti cheyabadina samaruupatalatoe automator yokka kanaalugaa upayoginchavacchu. udaaharanaku, oka dimensional line off selsnu eee vidhamgaa puurnaamkaala sankalana samuuhamgaa varninchavachhu, mariyu adhika dimensional integer gridlanu free abelian samuhaluga varninchavachhu.
oka samuuhampai cellular automator yokka anni saadhyamaina sthithula sekarananu prati samuuha muulakaanni varnamaalaloni chihnalalo okadaaniki mapp chese vidhulugaa varninchavachhu.
parimita samitigaa, varnamaala vivikta sthalavignaanaanni kaligi untundi, mariyu sthithula sekaranaku utpatti sthalavignaanam ivvavacchu (idhi vivikta sthalavignaanaala utpatti kabatti dheenini vivikta sthalavignaanam anie pilustaaru).
cellular automaton yokka parivartana vidhiga undalante, eee topologyki sthithula nundi sthithulaku oka vidhi nirantara vidhiga undaali, mariyu samuuha charyatho kooda samanamga undaali, antey parivartana vidhini vartimpajese mundu kanaalanu marchadam anedi vidhini vartimpajesi, aapai kanaalanu marchadam vanti phalitaanni utpatti chestundi. atuvanti functionla kosam, curtis-headlund-lindon siddhaantam prati samuuha moolakam vadda parivartana function viluva kevalam parimita porugu muulakaala samiti yokka munupati sthithipai aadharapadi untundani nirdhaaristundi.
prati raashtraaniki oka puurvagaami unnappudu (eeden thota undakudadu) oka rashtra parivartana vidhi anedi oka surjective vidhi. yea rendu sthithulu oke vaarasudini kaligi lenappudu idhi oka suudi charya. surjunctive group anedi daani muulakaalanu cellular automata kanaalugaa upayoginchinappudu, cellular automaton yokka prati injective transition function kooda surjectivega unde lakshanamtho kuudina samuuham.
samanamga, paina perkonna nirvachanaalanu sangrahinchi, prati parimita samiti suutram _ 2kii, prati nirantara samaanamaina suudi suutram suutram _ 3 kooda surjective ayithe, oka samuuha suutram _ 1 surjective avutundi. injectivity nundi surjectivityki chikkulu anedi eeden siddhaantam yokka thota yokka oka roopam, mariyu injective mariyu surjective transition functionla nundi nirvachinchabadina cellular automata reversible.
udaaharanalu.
surjunctive samuuhaala udaaharanalalo anni sthaanikamgaa avashesha parimita samuuhaalu, anni uchita samuuhaalu, surjunctive samuuhaala yokka anni upa samuuhaalu, anni abelian samuuhaalu, anni sophic samuuhaalu mariyu prati sthaanikamgaa surjunctive samuuham unnaayi.
1973loe athanu surjunctive groupulanu pravesapettinappudu, surjunctive kaani groupulaku telisina udaaharanalu levani gotschack gamaninchaaru. 2014 natiki, prati samuuham surjunctive avtunda anedi inca teliyadu.

