{"id":476352,"date":"2023-08-09T07:28:31","date_gmt":"2023-08-09T07:28:31","guid":{"rendered":""},"modified":"2023-09-05T11:12:34","modified_gmt":"2023-09-05T11:12:34","slug":"computational-complexity-theory","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/computational-complexity-theory\/","title":{"rendered":"L\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n"},"content":{"rendered":"

L\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n l\u00e0 m\u1ed9t nh\u00e1nh c\u1ee7a khoa h\u1ecdc m\u00e1y t\u00ednh nghi\u00ean c\u1ee9u c\u00e1c ngu\u1ed3n l\u1ef1c c\u1ea7n thi\u1ebft \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 t\u00ednh to\u00e1n. N\u00f3 cung c\u1ea5p s\u1ef1 tr\u1eebu t\u01b0\u1ee3ng v\u1ec1 m\u1eb7t to\u00e1n h\u1ecdc c\u1ee7a ph\u1ea7n c\u1ee9ng m\u00e1y t\u00ednh v\u00e0 ph\u00e2n t\u00edch c\u00e1c thu\u1eadt to\u00e1n, l\u00e0m cho n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t th\u00e0nh ph\u1ea7n quan tr\u1ecdng trong vi\u1ec7c hi\u1ec3u v\u00e0 \u0111\u00e1nh gi\u00e1 hi\u1ec7u qu\u1ea3 t\u00ednh to\u00e1n c\u1ee7a thu\u1eadt to\u00e1n c\u0169ng nh\u01b0 nh\u1eefng h\u1ea1n ch\u1ebf m\u00e0 m\u00e1y t\u00ednh c\u00f3 th\u1ec3 l\u00e0m.<\/p>\n

Ngu\u1ed3n g\u1ed1c c\u1ee7a l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n

S\u1ef1 xu\u1ea5t hi\u1ec7n c\u1ee7a L\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n nh\u01b0 m\u1ed9t l\u0129nh v\u1ef1c ri\u00eang bi\u1ec7t c\u00f3 th\u1ec3 b\u1eaft ngu\u1ed3n t\u1eeb nh\u1eefng n\u0103m 1950 v\u00e0 1960. Tuy nhi\u00ean, c\u00e1c nguy\u00ean t\u1eafc c\u01a1 b\u1ea3n c\u1ee7a n\u00f3 \u0111\u00e3 \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n k\u1ec3 t\u1eeb khi ra \u0111\u1eddi l\u00fd thuy\u1ebft khoa h\u1ecdc m\u00e1y t\u00ednh v\u00e0 l\u00fd thuy\u1ebft thu\u1eadt to\u00e1n. C\u1ed9t m\u1ed1c quan tr\u1ecdng nh\u1ea5t x\u1ea3y ra v\u00e0o n\u0103m 1965 khi Juris Hartmanis v\u00e0 Richard Stearns \u0111\u1ec1 xu\u1ea5t c\u00e1c l\u1edbp \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian P (Th\u1eddi gian \u0111a th\u1ee9c) v\u00e0 EXP (Th\u1eddi gian h\u00e0m m\u0169), kh\u1edfi \u0111\u1ea7u nghi\u00ean c\u1ee9u ch\u00ednh th\u1ee9c v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n. C\u00f4ng vi\u1ec7c c\u1ee7a h\u1ecd \u0111\u00e3 mang l\u1ea1i cho h\u1ecd gi\u1ea3i th\u01b0\u1edfng Turing v\u00e0o n\u0103m 1993.<\/p>\n

C\u00e2u h\u1ecfi P vs NP, m\u1ed9t trong nh\u1eefng b\u00e0i to\u00e1n ch\u01b0a gi\u1ea3i n\u1ed5i ti\u1ebfng nh\u1ea5t trong khoa h\u1ecdc m\u00e1y t\u00ednh, \u0111\u01b0\u1ee3c John Nash \u0111\u1ec1 c\u1eadp l\u1ea7n \u0111\u1ea7u ti\u00ean v\u00e0o n\u0103m 1955 v\u00e0 sau \u0111\u00f3 \u0111\u01b0\u1ee3c Stephen Cook v\u00e0 Leonid Levin ch\u00ednh th\u1ee9c h\u00f3a m\u1ed9t c\u00e1ch \u0111\u1ed9c l\u1eadp v\u00e0o n\u0103m 1971. B\u00e0i to\u00e1n n\u00e0y v\u1ec1 c\u01a1 b\u1ea3n l\u00e0 v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c b\u00e0i to\u00e1n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft nhanh ch\u00f3ng v\u00e0 nh\u1eefng gi\u1ea3i ph\u00e1p c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ki\u1ec3m tra nhanh ch\u00f3ng, \u0111\u00e3 th\u00fac \u0111\u1ea9y ph\u1ea7n l\u1edbn nghi\u00ean c\u1ee9u v\u1ec1 L\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n.<\/p>\n

\u0110i s\u00e2u v\u00e0o l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n

L\u00fd thuy\u1ebft v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n n\u00f3i v\u1ec1 vi\u1ec7c \u0111o l\u01b0\u1ee3ng t\u00e0i nguy\u00ean t\u00ednh to\u00e1n - ch\u1eb3ng h\u1ea1n nh\u01b0 th\u1eddi gian, b\u1ed9 nh\u1edb v\u00e0 giao ti\u1ebfp - c\u1ea7n thi\u1ebft \u0111\u1ec3 gi\u1ea3i quy\u1ebft m\u1ed9t v\u1ea5n \u0111\u1ec1. \u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo c\u00e1c ngu\u1ed3n l\u1ef1c \u0111\u01b0\u1ee3c y\u00eau c\u1ea7u b\u1edfi thu\u1eadt to\u00e1n t\u1ed1t nh\u1ea5t c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c v\u1ea5n \u0111\u1ec1.<\/p>\n

\u0110\u1ec3 \u0111o \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a thu\u1eadt to\u00e1n, ng\u01b0\u1eddi ta th\u01b0\u1eddng x\u00e1c \u0111\u1ecbnh k\u00edch th\u01b0\u1edbc \u0111\u1ea7u v\u00e0o (th\u01b0\u1eddng l\u00e0 s\u1ed1 bit c\u1ea7n thi\u1ebft \u0111\u1ec3 bi\u1ec3u th\u1ecb \u0111\u1ea7u v\u00e0o) v\u00e0 m\u00f4 t\u1ea3 t\u00e0i nguy\u00ean nh\u01b0 m\u1ed9t h\u00e0m c\u1ee7a k\u00edch th\u01b0\u1edbc \u0111\u1ea7u v\u00e0o. C\u00e1c l\u1edbp ph\u1ee9c t\u1ea1p ph\u00e2n lo\u1ea1i c\u00e1c v\u1ea5n \u0111\u1ec1 d\u1ef1a tr\u00ean l\u01b0\u1ee3ng t\u00e0i nguy\u00ean t\u00ednh to\u00e1n c\u1ee5 th\u1ec3 c\u1ea7n thi\u1ebft \u0111\u1ec3 gi\u1ea3i quy\u1ebft ch\u00fang. V\u00ed d\u1ee5 v\u1ec1 c\u00e1c l\u1edbp ph\u1ee9c t\u1ea1p bao g\u1ed3m P (c\u00e1c b\u00e0i to\u00e1n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i trong th\u1eddi gian \u0111a th\u1ee9c), NP (c\u00e1c b\u00e0i to\u00e1n c\u00f3 l\u1eddi gi\u1ea3i c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ki\u1ec3m tra trong th\u1eddi gian \u0111a th\u1ee9c) v\u00e0 NP-\u0111\u1ea7y \u0111\u1ee7 (c\u00e1c b\u00e0i to\u00e1n m\u00e0 b\u1ea5t k\u1ef3 b\u00e0i to\u00e1n NP n\u00e0o c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3m b\u1edbt trong th\u1eddi gian \u0111a th\u1ee9c).<\/p>\n

M\u1ed1i quan t\u00e2m ch\u00ednh trong L\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n l\u00e0 x\u00e1c \u0111\u1ecbnh \u0111\u1ed9 kh\u00f3 v\u1ed1n c\u00f3 c\u1ee7a c\u00e1c v\u1ea5n \u0111\u1ec1 t\u00ednh to\u00e1n, th\u01b0\u1eddng nh\u01b0ng kh\u00f4ng ph\u1ea3i l\u00fac n\u00e0o c\u0169ng \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n d\u01b0\u1edbi d\u1ea1ng \u0111\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian. M\u1ed9t b\u00e0i to\u00e1n \u0111\u01b0\u1ee3c coi l\u00e0 'kh\u00f3' n\u1ebfu th\u1eddi gian c\u1ea7n thi\u1ebft \u0111\u1ec3 gi\u1ea3i n\u00f3 t\u0103ng l\u00ean nhanh ch\u00f3ng khi k\u00edch th\u01b0\u1edbc c\u1ee7a \u0111\u1ea7u v\u00e0o t\u0103ng l\u00ean.<\/p>\n

C\u01a1 ch\u1ebf c\u1ee7a l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n

\u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch x\u00e2y d\u1ef1ng c\u00e1c m\u00f4 h\u00ecnh t\u00ednh to\u00e1n to\u00e1n h\u1ecdc v\u00e0 sau \u0111\u00f3 ph\u00e2n t\u00edch c\u00e1c m\u00f4 h\u00ecnh n\u00e0y. M\u00f4 h\u00ecnh ph\u1ed5 bi\u1ebfn nh\u1ea5t l\u00e0 m\u00e1y Turing, m\u1ed9t m\u00e1y tr\u1eebu t\u01b0\u1ee3ng x\u1eed l\u00fd c\u00e1c k\u00fd hi\u1ec7u tr\u00ean m\u1ed9t d\u1ea3i b\u0103ng theo m\u1ed9t b\u1ed9 quy t\u1eafc h\u1eefu h\u1ea1n.<\/p>\n

M\u1ed9t kh\u00eda c\u1ea1nh c\u01a1 b\u1ea3n c\u1ee7a \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n l\u00e0 kh\u00e1i ni\u1ec7m v\u1ec1 'l\u1edbp' c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1, l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c v\u1ea5n \u0111\u1ec1 c\u00f3 \u0111\u1ed9 ph\u1ee9c t\u1ea1p d\u1ef1a tr\u00ean t\u00e0i nguy\u00ean c\u00f3 li\u00ean quan. Nh\u01b0 \u0111\u00e3 \u0111\u1ec1 c\u1eadp tr\u01b0\u1edbc \u0111\u00f3, P, NP v\u00e0 NP-\u0111\u1ea7y \u0111\u1ee7 l\u00e0 nh\u1eefng v\u00ed d\u1ee5 v\u1ec1 c\u00e1c l\u1edbp v\u1ea5n \u0111\u1ec1. Vi\u1ec7c ph\u00e2n lo\u1ea1i c\u00e1c v\u1ea5n \u0111\u1ec1 theo c\u00e1ch n\u00e0y gi\u00fap ph\u00e1c h\u1ecda b\u1ed1i c\u1ea3nh v\u1ec1 nh\u1eefng g\u00ec kh\u1ea3 thi v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n v\u00e0 nh\u1eefng g\u00ec kh\u00f4ng.<\/p>\n

C\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n
    \n
  1. \n

    Ph\u00e2n lo\u1ea1i v\u1ea5n \u0111\u1ec1<\/strong>: L\u00fd thuy\u1ebft v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n ph\u00e2n lo\u1ea1i c\u00e1c v\u1ea5n \u0111\u1ec1 th\u00e0nh nhi\u1ec1u l\u1edbp kh\u00e1c nhau d\u1ef1a tr\u00ean \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a ch\u00fang.<\/p>\n<\/li>\n

  2. \n

    \u0110o l\u01b0\u1eddng m\u1ee9c s\u1eed d\u1ee5ng t\u00e0i nguy\u00ean<\/strong>: N\u00f3 cung c\u1ea5p m\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn to\u00e1n h\u1ecdc \u0111\u1ec3 \u0111o l\u01b0\u1eddng c\u00e1c t\u00e0i nguy\u00ean m\u00e0 thu\u1eadt to\u00e1n y\u00eau c\u1ea7u.<\/p>\n<\/li>\n

  3. \n

    Kh\u00f3 kh\u0103n c\u1ed1 h\u1eefu c\u1ee7a v\u1ea5n \u0111\u1ec1<\/strong>: N\u00f3 nghi\u00ean c\u1ee9u nh\u1eefng kh\u00f3 kh\u0103n v\u1ed1n c\u00f3 c\u1ee7a c\u00e1c v\u1ea5n \u0111\u1ec1 t\u00ednh to\u00e1n, b\u1ea5t k\u1ec3 thu\u1eadt to\u00e1n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft ch\u00fang.<\/p>\n<\/li>\n

  4. \n

    Gi\u1edbi h\u1ea1n t\u00ednh to\u00e1n<\/strong>: N\u00f3 t\u00ecm c\u00e1ch x\u00e1c \u0111\u1ecbnh ranh gi\u1edbi c\u1ee7a nh\u1eefng g\u00ec c\u00f3 th\u1ec3 v\u00e0 kh\u00f4ng th\u1ec3 t\u00ednh to\u00e1n.<\/p>\n<\/li>\n

  5. \n

    T\u00ednh to\u00e1n t\u01b0\u01a1ng \u0111\u01b0\u01a1ng<\/strong>: N\u00f3 ti\u1ebft l\u1ed9 s\u1ef1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1ec1 m\u1eb7t t\u00ednh to\u00e1n b\u1eb1ng c\u00e1ch ch\u1ec9 ra c\u00e1ch c\u00e1c v\u1ea5n \u0111\u1ec1 kh\u00e1c nhau c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c chuy\u1ec3n \u0111\u1ed5i ho\u1eb7c gi\u1ea3m b\u1edbt l\u1eabn nhau.<\/p>\n<\/li>\n<\/ol>\n

    C\u00e1c lo\u1ea1i th\u01b0\u1edbc \u0111o \u0111\u1ed9 ph\u1ee9c t\u1ea1p kh\u00e1c nhau<\/h2>\n

    C\u00f3 nhi\u1ec1u c\u00e1ch kh\u00e1c nhau \u0111\u1ec3 \u0111o l\u01b0\u1eddng \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1 v\u00e0 m\u1ed7i lo\u1ea1i th\u01b0\u1edbc \u0111o c\u00f3 th\u1ec3 t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t m\u1ee9c \u0111\u1ed9 ph\u1ee9c t\u1ea1p kh\u00e1c nhau.<\/p>\n\n\n\n\n\n\n\n\n\n
    Ki\u1ec3u<\/th>\nS\u1ef1 mi\u00eau t\u1ea3<\/th>\n<\/tr>\n<\/thead>\n
    \u0110\u1ed9 ph\u1ee9c t\u1ea1p th\u1eddi gian<\/td>\n\u0110o th\u1eddi gian t\u00ednh to\u00e1n c\u1ee7a m\u1ed9t thu\u1eadt to\u00e1n.<\/td>\n<\/tr>\n
    \u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a kh\u00f4ng gian<\/td>\n\u0110o l\u01b0\u1ee3ng b\u1ed9 nh\u1edb \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng b\u1edfi m\u1ed9t thu\u1eadt to\u00e1n.<\/td>\n<\/tr>\n
    \u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a giao ti\u1ebfp<\/td>\n\u0110o l\u01b0\u1ee3ng giao ti\u1ebfp c\u1ea7n thi\u1ebft cho t\u00ednh to\u00e1n ph\u00e2n t\u00e1n.<\/td>\n<\/tr>\n
    \u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ea1ch<\/td>\n\u0110o k\u00edch th\u01b0\u1edbc c\u1ee7a m\u1ea1ch boolean \u0111\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1.<\/td>\n<\/tr>\n
    \u0110\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a c\u00e2y quy\u1ebft \u0111\u1ecbnh<\/td>\n\u0110o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 ph\u1ee9c t\u1ea1p c\u1ee7a m\u1ed9t v\u1ea5n \u0111\u1ec1 trong m\u00f4 h\u00ecnh trong \u0111\u00f3 m\u00e1y t\u00ednh ch\u1ec9 c\u00f3 th\u1ec3 \u0111\u01b0a ra c\u00e1c quy\u1ebft \u0111\u1ecbnh nh\u1ecb ph\u00e2n \u0111\u01a1n gi\u1ea3n.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u1ee8ng d\u1ee5ng, th\u00e1ch th\u1ee9c v\u00e0 gi\u1ea3i ph\u00e1p trong l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n

    L\u00fd thuy\u1ebft n\u00e0y c\u00f3 \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong thi\u1ebft k\u1ebf thu\u1eadt to\u00e1n, m\u1eadt m\u00e3, c\u1ea5u tr\u00fac d\u1eef li\u1ec7u, v.v. N\u00f3 gi\u00fap thi\u1ebft k\u1ebf c\u00e1c thu\u1eadt to\u00e1n hi\u1ec7u qu\u1ea3 b\u1eb1ng c\u00e1ch cung c\u1ea5p gi\u1edbi h\u1ea1n tr\u00ean cho c\u00e1c t\u00e0i nguy\u00ean t\u00ednh to\u00e1n c\u1ea7n thi\u1ebft.<\/p>\n

    M\u1ed9t th\u00e1ch th\u1ee9c l\u1edbn trong l\u0129nh v\u1ef1c n\u00e0y l\u00e0 thi\u1ebfu b\u1eb1ng ch\u1ee9ng ch\u00ednh th\u1ee9c cho m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi quan tr\u1ecdng nh\u1ea5t, nh\u01b0 b\u00e0i to\u00e1n P v\u00e0 NP. B\u1ea5t ch\u1ea5p nh\u1eefng th\u00e1ch th\u1ee9c n\u00e0y, s\u1ef1 ph\u00e1t tri\u1ec3n v\u00e0 c\u1ea3i ti\u1ebfn li\u00ean t\u1ee5c c\u1ee7a c\u00e1c k\u1ef9 thu\u1eadt ch\u1ee9ng minh, m\u00f4 h\u00ecnh t\u00ednh to\u00e1n v\u00e0 c\u00e1c l\u1edbp ph\u1ee9c t\u1ea1p \u0111ang d\u1ea7n m\u1edf r\u1ed9ng hi\u1ec3u bi\u1ebft c\u1ee7a ch\u00fang ta v\u1ec1 gi\u1edbi h\u1ea1n t\u00ednh to\u00e1n.<\/p>\n

    So s\u00e1nh v\u00e0 \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh<\/h2>\n

    S\u1ef1 so s\u00e1nh gi\u1eefa c\u00e1c l\u1edbp \u0111\u1ed9 ph\u1ee9c t\u1ea1p kh\u00e1c nhau t\u1ea1o th\u00e0nh \u0111i\u1ec3m m\u1ea5u ch\u1ed1t c\u1ee7a l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n.<\/p>\n\n\n\n\n\n\n\n\n
    L\u1edbp h\u1ecdc<\/th>\nS\u1ef1 mi\u00eau t\u1ea3<\/th>\n<\/tr>\n<\/thead>\n
    P<\/td>\nC\u00e1c b\u00e0i to\u00e1n c\u00f3 th\u1ec3 gi\u1ea3i nhanh (trong th\u1eddi gian \u0111a th\u1ee9c)<\/td>\n<\/tr>\n
    NP<\/td>\nC\u00e1c v\u1ea5n \u0111\u1ec1 m\u00e0 m\u1ed9t gi\u1ea3i ph\u00e1p \u0111\u01b0\u1ee3c \u0111\u01b0a ra c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ki\u1ec3m tra nhanh ch\u00f3ng<\/td>\n<\/tr>\n
    NP-Ho\u00e0n th\u00e0nh<\/td>\nNh\u1eefng v\u1ea5n \u0111\u1ec1 kh\u00f3 kh\u0103n nh\u1ea5t \u1edf NP; m\u1ed9t gi\u1ea3i ph\u00e1p cho m\u1ed9t v\u1ea5n \u0111\u1ec1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft t\u1ea5t c\u1ea3 nh\u1eefng gi\u1ea3i ph\u00e1p kh\u00e1c trong NP<\/td>\n<\/tr>\n
    EXP<\/td>\nC\u00e1c v\u1ea5n \u0111\u1ec1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft theo th\u1eddi gian theo c\u1ea5p s\u1ed1 nh\u00e2n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Vi\u1ec5n c\u1ea3nh t\u01b0\u01a1ng lai v\u00e0 ti\u1ebfn b\u1ed9 c\u00f4ng ngh\u1ec7<\/h2>\n

    \u0110i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed v\u00e0 h\u1ecdc m\u00e1y \u0111ang \u0111\u1ecbnh h\u00ecnh t\u01b0\u01a1ng lai c\u1ee7a L\u00fd thuy\u1ebft v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n. \u0110i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed, v\u1edbi ti\u1ec1m n\u0103ng gi\u1ea3i quy\u1ebft m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 nhanh h\u01a1n m\u00e1y t\u00ednh c\u1ed5 \u0111i\u1ec3n, \u0111ang th\u00fac \u0111\u1ea9y vi\u1ec7c \u0111\u00e1nh gi\u00e1 l\u1ea1i c\u00e1c l\u1edbp ph\u1ee9c t\u1ea1p \u0111\u00e3 \u0111\u01b0\u1ee3c thi\u1ebft l\u1eadp. M\u1eb7t kh\u00e1c, h\u1ecdc m\u00e1y \u0111\u01b0a ra c\u00e1c lo\u1ea1i c\u00e2u h\u1ecfi m\u1edbi li\u00ean quan \u0111\u1ebfn t\u00e0i nguy\u00ean, d\u1eabn \u0111\u1ebfn s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a c\u00e1c l\u1edbp v\u00e0 th\u01b0\u1edbc \u0111o \u0111\u1ed9 ph\u1ee9c t\u1ea1p m\u1edbi.<\/p>\n

    Proxy v\u00e0 l\u00fd thuy\u1ebft \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/h2>\n

    Trong b\u1ed1i c\u1ea3nh m\u00e1y ch\u1ee7 proxy, L\u00fd thuy\u1ebft v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n c\u00f3 th\u1ec3 gi\u00fap t\u1ed1i \u01b0u h\u00f3a vi\u1ec7c x\u1eed l\u00fd c\u00e1c y\u00eau c\u1ea7u. Hi\u1ec3u \u0111\u01b0\u1ee3c \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n c\u1ee7a thu\u1eadt to\u00e1n \u0111\u1ecbnh tuy\u1ebfn c\u00f3 th\u1ec3 d\u1eabn \u0111\u1ebfn thi\u1ebft k\u1ebf hi\u1ec7u qu\u1ea3 h\u01a1n v\u00e0 c\u00e2n b\u1eb1ng t\u1ea3i t\u1ed1t h\u01a1n. Ngo\u00e0i ra, l\u00fd thuy\u1ebft ph\u1ee9c t\u1ea1p c\u00f3 th\u1ec3 h\u1ed7 tr\u1ee3 thi\u1ebft k\u1ebf b\u1ea3o m\u1eadt m\u1ea1nh m\u1ebd cho proxy, trong \u0111\u00f3 c\u00e1c giao th\u1ee9c m\u1eadt m\u00e3 \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng.<\/p>\n

    Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n
      \n
    1. B\u00e1ch khoa to\u00e0n th\u01b0 Stanford v\u1ec1 tri\u1ebft h\u1ecdc: L\u00fd thuy\u1ebft v\u1ec1 \u0111\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n<\/a><\/li>\n
    2. \u0110\u1ed9 ph\u1ee9c t\u1ea1p t\u00ednh to\u00e1n: C\u00e1ch ti\u1ebfp c\u1eadn hi\u1ec7n \u0111\u1ea1i c\u1ee7a Sanjeev Arora v\u00e0 Boaz Barak<\/a><\/li>\n
    3. Trang P vs NP<\/a><\/li>\n<\/ol>","protected":false},"featured_media":467942,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476352","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Computational Complexity Theory: Unfolding the Intricacies of Computational Power and Efficiency<\/mark>","faq_items":[{"question":"What is Computational Complexity Theory?","answer":"

      Computational Complexity Theory is a branch of computer science that deals with the resources required to solve computational problems. It helps understand and assess the computational efficiency of algorithms and the limitations of computing.<\/p>"},{"question":"When and how did Computational Complexity Theory originate?","answer":"

      Computational Complexity Theory originated as a distinct field in the 1950s and 1960s, but its principles were being developed from the start of theoretical computer science. The significant milestone was in 1965 when Juris Hartmanis and Richard Stearns proposed the time complexity classes P and EXP.<\/p>"},{"question":"What are the key features of Computational Complexity Theory?","answer":"

      The key features of Computational Complexity Theory include problem classification, measurement of resource usage, determination of inherent problem difficulty, identification of computational limits, and discovery of computational equivalences.<\/p>"},{"question":"What types of complexity measures exist in Computational Complexity Theory?","answer":"

      Several complexity measures exist, such as Time Complexity (computational time taken), Space Complexity (memory usage), Communication Complexity (required communication for distributed computation), Circuit Complexity (size of a boolean circuit that solves the problem), and Decision Tree Complexity (complexity of a problem in a binary decision-making model).<\/p>"},{"question":"How is Computational Complexity Theory used, and what are some related challenges?","answer":"

      Computational Complexity Theory finds applications in algorithm design, cryptography, data structures, and more. The major challenge in the field is the lack of formal proofs for crucial questions like the P vs NP problem. Continuous development of proof techniques, computational models, and complexity classes help address these challenges.<\/p>"},{"question":"How does Computational Complexity Theory relate to future technologies like Quantum Computing and Machine Learning?","answer":"

      Quantum computing, capable of solving certain problems faster than classical computers, prompts reevaluation of established complexity classes. Machine learning presents new types of resource-related questions, leading to the development of new complexity measures and classes.<\/p>"},{"question":"What is the relevance of Computational Complexity Theory to Proxy Servers?","answer":"

      Understanding the computational complexity of routing algorithms can lead to more efficient design and better load balancing in proxy servers. Complexity theory can also assist in robust security design for proxies where cryptographic protocols play a vital role.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476352","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476352\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/467942"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}