{"id":31157,"date":"2019-10-31T21:39:48","date_gmt":"2019-10-31T18:39:48","guid":{"rendered":"https:\/\/prohoster.info\/blog\/paradoksy-o-szhatii-dannyh\/"},"modified":"2019-10-31T21:39:48","modified_gmt":"2019-10-31T18:39:48","slug":"paradoksy-o-szhatii-dannyh","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sq\/blog\/administrirovanie\/paradoksy-o-szhatii-dannyh","title":{"rendered":"Paradokset mbi kompresimin e t\u00eb dh\u00ebnave","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Paradokset mbi kompresimin e t\u00eb dh\u00ebnave\" src=\"\/wp-content\/uploads\/2019\/04\/d15fed5cc55334e6bb9bc3bbd7cbf50c.jpeg\" style=\"display:block;margin: 0 auto;\" \/> Detyra e kompresimit t\u00eb t\u00eb dh\u00ebnave n\u00eb form\u00ebn e saj m\u00eb t\u00eb thjesht\u00eb mund t\u00eb lidhet me numrat dhe p\u00ebrfaq\u00ebsimet e tyre. Numrat mund t\u00eb p\u00ebrfaq\u00ebsohen me numra (<i>\u00abnj\u00ebmb\u00ebdhjet\u00eb\u00bb<\/i> p\u00ebr numrin 11), shprehje matematike (<i>\u00abdy n\u00eb nj\u00ebzet\u00ebn\u00bb<\/i> p\u00ebr 1048576), shprehje string (<i>\u00abpes\u00eb n\u00ebntat\u00bb<\/i> p\u00ebr 99999), emra t\u00eb ve\u00e7ant\u00eb (<i>\u00abnumri i bish\u00ebs\u00bb<\/i> p\u00ebr 666, <i>\u00abviti i vdekjes s\u00eb Turing\u00bb<\/i> p\u00ebr 1954), ose kombinime t\u00eb tyre t\u00eb rast\u00ebsishme. \u00c7do p\u00ebrfaq\u00ebsim \u00ebsht\u00eb i pranuesh\u00ebm, me kusht q\u00eb diskutuesi t\u00eb jet\u00eb i aft\u00eb t\u00eb p\u00ebrcaktoj\u00eb qart\u00eb se cila \u00ebsht\u00eb numri n\u00eb fjal\u00eb. \u00cbsht\u00eb e dukshme se t'i thuash diskutuesit <i>\u00abfaktoriali i tet\u00eb\u00bb<\/i> \u00ebsht\u00eb m\u00eb efikase se sa p\u00ebrfaq\u00ebsimi ekuivalent <i>\u00abdyzet mij\u00eb triqind e nj\u00ebzet\u00bb<\/i>. K\u00ebtu lind nj\u00eb pyetje logjike: cila \u00ebsht\u00eb p\u00ebrfaq\u00ebsimi m\u00eb i shkurt\u00ebr p\u00ebr nj\u00eb num\u00ebr t\u00eb caktuar?<\/p>\n<p>Filozofi Bertrand Russell publikoi n\u00eb 1908 <noindex><a rel=\"nofollow\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81_%D0%91%D0%B5%D1%80%D1%80%D0%B8\">\u00abparadoksin Berry\u00bb<\/a><\/noindex>, i cili shqyrton pyetjen e p\u00ebrfaq\u00ebsimeve t\u00eb numrave nga nj\u00eb an\u00eb tjet\u00ebr: <b>cili \u00ebsht\u00eb numri m\u00eb i vog\u00ebl p\u00ebr t\u00eb cilin nuk jan\u00eb t\u00eb mjaftueshme tet\u00ebdhjet\u00eb letra?<\/b><br \/>\nN\u00eb fakt, ky num\u00ebr duhet t\u00eb ekzistoj\u00eb: me tet\u00ebdhjet\u00eb shkronjat ruse dhe hap\u00ebsirat mund t\u00eb krijohen vet\u00ebm 3480 p\u00ebrfaq\u00ebsime, dometh\u00ebn\u00eb, duke p\u00ebrdorur tet\u00ebdhjet\u00eb shkronja, nuk mund t\u00eb p\u00ebrfaq\u00ebsojm\u00eb m\u00eb shum\u00eb se 3480 numra. Pra, nj\u00eb num\u00ebr q\u00eb \u00ebsht\u00eb m\u00eb i vog\u00ebl se 3480 nuk mund t\u00eb p\u00ebrfaq\u00ebsohet n\u00eb k\u00ebt\u00eb m\u00ebnyr\u00eb.<\/p>\n<p>K\u00ebshtu, k\u00ebtij numri do t'i p\u00ebrkas\u00eb p\u00ebrfaq\u00ebsimi <i>\u00abnumri m\u00eb i vog\u00ebl p\u00ebr t\u00eb cilin nuk jan\u00eb t\u00eb mjaftueshme tet\u00ebdhjet\u00eb letra\u00bb<\/i>, i cili ka gjithsej 78 shkronja! Nga nj\u00ebra an\u00eb, ky num\u00ebr duhet t\u00eb ekzistoj\u00eb; nga ana tjet\u00ebr, n\u00ebse ky num\u00ebr ekziston, p\u00ebrfaq\u00ebsimi i tij nuk i korrespondon. Paradoksi!<noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><\/p>\n<p>M\u00ebnyra m\u00eb e thjesht\u00eb p\u00ebr t\u00eb anashkaluar k\u00ebt\u00eb paradoks \u00ebsht\u00eb t\u00eb referohemi n\u00eb informalitetin e p\u00ebrfaq\u00ebsimeve verbale. Sipas k\u00ebsaj logjike, n\u00ebse n\u00eb p\u00ebrfaq\u00ebsime do t\u00eb lejohej vet\u00ebm nj\u00eb grup i miratur shprehjesh, at\u00ebher\u00eb <i>\u00abnumri m\u00eb i vog\u00ebl p\u00ebr t\u00eb cilin nuk jan\u00eb t\u00eb mjaftueshme tet\u00ebdhjet\u00eb letra\u00bb<\/i> nuk do t\u00eb ishin p\u00ebrfaq\u00ebsime t\u00eb lejuara, nd\u00ebrsa p\u00ebrfaq\u00ebsime praktikisht t\u00eb dobishme si <i>\u00abfaktoriali i tet\u00eb\u00bb<\/i> do t\u00eb mbeteshin t\u00eb lejuesh\u00ebm.<\/p>\n<p>A ekzistojn\u00eb m\u00ebnyra formale p\u00ebr t\u00eb p\u00ebrshkruar nj\u00eb sekuenc\u00eb (algoritmi) t\u00eb veprimeve mbi numrat? Po, dhe n\u00eb boll\u00ebk \u2014 quhen gjuh\u00eb programuese. Le t\u00eb p\u00ebrdorim programe (p.sh., n\u00eb Python) n\u00eb vend t\u00eb p\u00ebrfaq\u00ebsimeve verbale p\u00ebr t\u00eb prodhuar numrat e nevojsh\u00ebm. P\u00ebr shembull, p\u00ebr pes\u00eb n\u00ebntat do t\u00eb ishte e duhura programi <code>print(\"9\"*5)<\/code>. Edhe nj\u00eb her\u00eb, do t\u00eb interesoheshim p\u00ebr programin m\u00eb t\u00eb shkurt\u00ebr p\u00ebr nj\u00eb num\u00ebr t\u00eb caktuar. Gjat\u00ebsia e k\u00ebtij programi quhet <noindex><a rel=\"nofollow\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D0%BE%D0%BB%D0%BC%D0%BE%D0%B3%D0%BE%D1%80%D0%BE%D0%B2%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%8C\">kompleksiteti kolmogorovian<\/a><\/noindex> i numrit; ky \u00ebsht\u00eb kufiri teorik deri ku nj\u00eb num\u00ebr i caktuar mund t\u00eb kompresohet.<\/p>\n<p>N\u00eb vend t\u00eb paradoksit Berry tani mund t\u00eb shqyrtojm\u00eb nj\u00eb t\u00eb ngjash\u00ebm: <b>cili \u00ebsht\u00eb numri m\u00eb i vog\u00ebl p\u00ebr t\u00eb cilin nuk jan\u00eb t\u00eb mjaftueshme nj\u00eb program i vog\u00ebl?<\/b><\/p>\n<p>Do t\u00eb argumentohemi ashtu si m\u00eb par\u00eb: ekzistojn\u00eb 2561024 tekste t\u00eb vogla, dometh\u00ebn\u00eb, me programet e vogla mund t\u00eb prodhojm\u00eb jo m\u00eb shum\u00eb se 2561024 numra. K\u00ebshtu, nj\u00eb num\u00ebr q\u00eb \u00ebsht\u00eb m\u00eb i vog\u00ebl se 2561024 nuk mund t\u00eb prodhohet n\u00eb k\u00ebt\u00eb m\u00ebnyr\u00eb.<\/p>\n<p>Por le t\u00eb shkruajm\u00eb nj\u00eb program n\u00eb Python q\u00eb gjeneron t\u00eb gjith\u00eb tekstet e mundshme t\u00eb vogla, i ekzekuton ato, dhe n\u00ebse ato prodhojn\u00eb nj\u00eb num\u00ebr \u2014 at\u00ebher\u00eb e shton k\u00ebt\u00eb num\u00ebr n\u00eb fjalorin e arritjes. Pas kontrollimit t\u00eb t\u00eb gjitha 2561024 mund\u00ebsive, sado koh\u00eb t\u00eb zgjas\u00eb \u2014 programi k\u00ebrkon cila \u00ebsht\u00eb numri m\u00eb i vog\u00ebl q\u00eb mungon n\u00eb fjalor dhe e prodhon at\u00eb num\u00ebr. Duket e qart\u00eb se nj\u00eb program i till\u00eb do t\u00eb futet n\u00eb nj\u00eb kilobajt kodi \u2014 dhe do t\u00eb prodhoj\u00eb at\u00eb num\u00ebr, i cili nuk mund t\u00eb prodhohet nga nj\u00eb program i vog\u00ebl!<\/p>\n<p>\u00c7far\u00eb ka ndodhur tani? Nuk mund t\u00eb anashkalohet informaliteti i p\u00ebrfaq\u00ebsimeve!<\/p>\n<p>N\u00ebse ju shqet\u00ebson fakti se programi yn\u00eb do t\u00eb k\u00ebrkoj\u00eb nj\u00eb sasi astronomike memorjeje p\u00ebr t\u00eb funksionuar \u2014 nj\u00eb fjalor (ose nj\u00eb matric\u00eb bit) me 2561024 elemente \u2014 at\u00ebher\u00eb mund ta realizoni t\u00eb gjith\u00eb at\u00eb edhe pa t\u00eb: p\u00ebr \u00e7do num\u00ebr nga 2561024 t\u00eb kontrolloni t\u00eb gjitha programet e mundshme t\u00eb vogla, derisa t\u00eb gjejm\u00eb nj\u00eb t\u00eb p\u00ebrshtatshme. Nuk ka r\u00ebnd\u00ebsi se sa do t\u00eb zgjas\u00eb ky kontroll: pasi kontrollimi i m\u00eb pak se (2561024)2 \u00e7ifteve t\u00eb numrit dhe programit, ai do t\u00eb p\u00ebrfundoj\u00eb, dhe do t\u00eb gjej\u00eb at\u00eb numrin e k\u00ebrkuar.<\/p>\n<p>Ose ndoshta nuk do t\u00eb p\u00ebrfundoj\u00eb? Sepse midis t\u00eb gjith\u00eb programeve q\u00eb do t\u00eb provosh, do t\u00eb has\u00ebsh <code>while True: pass<\/code> (dhe analog\u00ebt e saj funksional\u00eb) \u2014 dhe m\u00eb pas nuk do t\u00eb jet\u00eb m\u00eb e mundur p\u00ebr t\u00eb vazhduar kontrollin e k\u00ebtij programi!<\/p>\n<p>N\u00eb kund\u00ebrshtim me paradoksin Berry, ku hile ishte informaliteti i p\u00ebrfaq\u00ebsimeve, n\u00eb k\u00ebt\u00eb rast ne kemi nj\u00eb riformulim t\u00eb mir\u00eb maskuar t\u00eb <noindex><a rel=\"nofollow\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9F%D1%80%D0%BE%D0%B1%D0%BB%D0%B5%D0%BC%D0%B0_%D0%BE%D1%81%D1%82%D0%B0%D0%BD%D0%BE%D0%B2%D0%BA%D0%B8\">\u00abproblemit t\u00eb ndalimit\u00bb<\/a><\/noindex>. Problemi \u00ebsht\u00eb se me programin nuk \u00ebsht\u00eb e mundur t\u00eb p\u00ebrcaktosh produktin e tij brenda nj\u00eb kohe t\u00eb caktuar. N\u00eb ve\u00e7anti, kompleksiteti kolmogorovian <noindex><a rel=\"nofollow\" href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%92%D1%8B%D1%87%D0%B8%D1%81%D0%BB%D0%B8%D0%BC%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F\">nuk \u00ebsht\u00eb i llogaritsh\u00ebm.<\/a><\/noindex>: nuk ka asnj\u00eb algorit\u00ebm q\u00eb mund t\u00eb gjej\u00eb p\u00ebr nj\u00eb num\u00ebr t\u00eb caktuar gjat\u00ebsi e programit m\u00eb t\u00eb shkurt\u00ebr q\u00eb e printon at\u00eb num\u00ebr; prandaj, nuk ka asnj\u00eb zgjidhje as p\u00ebr problemin Berry \u2014 t\u00eb gjej\u00eb p\u00ebr nj\u00eb num\u00ebr t\u00eb caktuar gjat\u00ebsi e p\u00ebrshkrimit m\u00eb t\u00eb shkurt\u00ebr verbal.<br \/>\n<br \/>Burimi: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/446976\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u0417\u0430\u0434\u0430\u0447\u0430 \u0441\u0436\u0430\u0442\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 \u0432 \u0441\u0432\u043e\u0435\u0439 \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0435\u0439 \u0444\u043e\u0440\u043c\u0435 \u043c\u043e\u0436\u0435\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u044c\u0441\u044f \u043a \u0447\u0438\u0441\u043b\u0430\u043c \u0438 \u0438\u0445 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c. \u0427\u0438\u0441\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0442\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 (\u00ab\u043e\u0434\u0438\u043d\u043d\u0430\u0434\u0446\u0430\u0442\u044c\u00bb \u0434\u043b\u044f \u0447\u0438\u0441\u043b\u0430 11), \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438 (\u00ab\u0434\u0432\u0430 \u0432 \u0434\u0432\u0430\u0434\u0446\u0430\u0442\u043e\u0439\u00bb \u0434\u043b\u044f 1048576), \u0441\u0442\u0440\u043e\u043a\u043e\u0432\u044b\u043c\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438 (\u00ab\u043f\u044f\u0442\u044c \u0434\u0435\u0432\u044f\u0442\u043e\u043a\u00bb \u0434\u043b\u044f 99999), \u0438\u043c\u0435\u043d\u0430\u043c\u0438 \u0441\u043e\u0431\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c\u0438 (\u00ab\u0447\u0438\u0441\u043b\u043e \u0437\u0432\u0435\u0440\u044f\u00bb \u0434\u043b\u044f 666, \u00ab\u0433\u043e\u0434 \u0441\u043c\u0435\u0440\u0442\u0438 \u0422\u044c\u044e\u0440\u0438\u043d\u0433\u0430\u00bb \u0434\u043b\u044f 1954), \u0438\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u044b\u043c\u0438 \u0438\u0445 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f\u043c\u0438. \u0413\u043e\u0434\u0438\u0442\u0441\u044f \u043b\u044e\u0431\u043e\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u043e \u043a\u043e\u0442\u043e\u0440\u043e\u043c\u0443 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":23125,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[688],"tags":[],"class_list":["post-31157","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-administrirovanie"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0417\u0430\u0434\u0430\u0447\u0430 \u0441\u0436\u0430\u0442\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 \u0432 \u0441\u0432\u043e\u0435\u0439 \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0435\u0439 \u0444\u043e\u0440\u043c\u0435 \u043c\u043e\u0436\u0435\u0442 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u044c\u0441\u044f \u043a \u0447\u0438\u0441\u043b\u0430\u043c \u0438 \u0438\u0445 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