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Video, P vs. NP sorusunun çözümünün toplumsal etkileri ve bu sorunun teorik önemi üzerine düşüncelerle sonlanır."]},"endTime":609,"title":"P vs. NP: Bilgisayar Biliminin En Ünlü Açık Problemi","beginTime":0}],"fullResult":[{"index":0,"title":"P vs NP Problemi","list":{"type":"unordered","items":["P vs NP, bilgisayar biliminde en ünlü açık problemlerden biridir ve problem çözme doğasını, Mario ile şifreleme arasında bağlantı kurar.","P vs NP, kolay anlaşılan ancak zor çözülen matematik problemlerini tanımlar ve temel sorusu \"jigsaw puzzle'ları kolayca çözebilir miyiz?\" şeklinde özetlenebilir.","Bilgisayar biliminde problemler, çözümlerinin zorluğuna göre P ve NP olarak kategorize edilir."]},"beginTime":0,"endTime":38,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=0&ask_summarization=1"},{"index":1,"title":"P ve NP Problemleri","list":{"type":"unordered","items":["P sınıfı, çözümü kolay ve 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problemlerdir."]},"beginTime":127,"endTime":214,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=127&ask_summarization=1"},{"index":3,"title":"SAT ve NP Tamamlama","list":{"type":"unordered","items":["Cook-Levin teoremi, SAT (Satisfiability Problemi) adlı problemi NP sınıfındaki en zor problem olarak tanımlar.","SAT, NP sınıfındaki tüm problemleri temsil edebilir ve herhangi bir NP problemi SAT'a dönüştürülebilir.","SAT'ı kolayca çözebilirsek, tüm NP problemlerini kolayca çözebilir ve P = NP olur; aksi takdirde P ≠ NP olur."]},"beginTime":214,"endTime":275,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=214&ask_summarization=1"},{"index":4,"title":"NP Tamamlama Problemleri","list":{"type":"unordered","items":["SAT, NP sınıfındaki tüm problemleri temsil edebilen \"NP tamamlama\" problemidir.","SAT'ın yanı sıra, puzzle çözme, Sudoku, Mario, Hamiltonian yol bulma ve alt toplam bulma gibi birçok NP tamamlama problemi vardır.","Tüm NP tamamlama problemleri temelde aynıdır çünkü birbirlerini çözebilirler."]},"beginTime":275,"endTime":353,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=275&ask_summarization=1"},{"index":5,"title":"Diğer Zor Problemler","list":{"type":"unordered","items":["P ve NP sınıflarının dışında, çözümü zor ancak doğrulanması da zor olan problemler vardır, örneğin satranç.","Bu tür problemler \"Exponential\" (EXP) sınıfına aittir ve P ile EXP arasında kesin bir ilişki yoktur.","Karmaşıklık teorisi alanında, alan kullanımı, problem tamamlama, probabilistik algoritmalar ve kuantum bilgisayarlar gibi farklı gruplar da bulunmaktadır."]},"beginTime":353,"endTime":444,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=353&ask_summarization=1"},{"index":6,"title":"P vs NP'nin Önemi","list":{"type":"unordered","items":["P = NP olsaydı, birçok zor problem kolayca çözülebilirdi ve bu da kripto şifrelemeyi geçersiz kılabilirdi.","NP tamamlama problemleri biyoloji, sanat galerileri ve sağlık alanlarında da görülmektedir.","P = NP olsaydı, bilgisayarlar matematiksel kanıtları hızlıca doğrulayabilirdi."]},"beginTime":444,"endTime":499,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=444&ask_summarization=1"},{"index":7,"title":"P vs NP'nin Gerçekçi Yaklaşımı","list":{"type":"unordered","items":["Çoğu bilgisayar bilimcisi P ≠ NP olduğunu düşünmektedir çünkü sürekli daha fazla NP tamamlama problemi keşfedilmektedir.","P = NP olsa bile, polinomel sürede çalışan bir algoritma hala çok yavaş olabilir.","NP tamamlama problemlerinin imkansız olmadığı, bilgisayarların bazı NP tamamlama problemlerini (örneğin standart Sudoku) hızlıca çözebildiği ve etkili yaklaşık çözüm algoritmaları geliştirildiği bilinmektedir."]},"beginTime":499,"endTime":590,"href":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=499&ask_summarization=1"}],"linkTemplate":"/video/preview/13014358928463202868?parent-reqid=1769521305821517-9398704609449850611-balancer-l7leveler-kubr-yp-klg-164-BAL&text=NP&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"P vs. NP - An 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