M CO diTng hay khong tren w la yeu to quyet dinh su ton tai thuat
96 May Turing vh Thuat toan
(A/i) (A/2) (A/3) (A/4)
A/i
A/2 A/3 A/3 A/4
accept accept accept accept accept accept
accept accept
B a n g 1.9 Tai giao diem giQa hang i vh CQt j dien accept
neu Mi chap nhan (A/j)
Trong bang sau day thg hien ket qua tinh toan cua may H trgn nhflng dau vao tudng ling v6i Bang 1.9. Chang han, neu may A/3 khong chap nhan dau vao (A/2), tai giao digm giita hang A/3 va cot
(A/2) t a dien reject bdi v i H bac bo (Afg, ( A / 2 ) ) .
(A/i) (A/3) (A/4)
A/i accept reject accept reject
A/2 accept accept accept accept
A/a reject reject reject reject
A/4 accept accept reject reject
B a n g 1.10 Hanh v i cua may H. Tai giao digm gifla hang i va cot J dien accept neu H chap nhan (A/j, (A/j))
Trong bang cuoi ciing, Bang 1.11 sau day, ta hay xem xet hanh v i cua C trong Bang 1.10. Theo gia thigt phan chiing, H la mot may Turing va do do C cung thg. B5i vay no phai xuat hien trong danh sach Ah, M2,... gom t a t ca cac may Turing. Tai digm dau hoi tren dvrdng cheo xuat hien mau thuan.
1.4 Mot vdi bdi toan khong gidi duoc 97
(A/i) (A/2) (A/3) (A/4) • • (C) A/i accept reject accept reject accept
A/2 accept accept accept accept reject
A/3 reject reject reject reject accept
A/4 accept accept reject reject accept
C reject accept reject accept ?
B a n g 1.11 Neu C c6 trong danh sach, mau thuan xuat hien t a i ?
• N g o n ngỉ k h o n g doan n h a n diTdc
Tren day ta da chi ra mot ngon ngiJ khong khang dinh diTOc, cu thg
la ngon ngu: A-ru- Bay gid ta gidi thieu mot ngon ngu: ma tham chi la khong doan nhan dudc. Nhan thay rang ngon ngfl A-YU khong
thg dap ling chu dinh nay, bdi v i t a da xay dung dUdc may Turing
van nang U dg doan nhan Aru- Dinh ly sau day chiing to rang, neu mot ngon ngfl va phan bii cua no deu la doan nhan dudc t h i
ngon ngfl ay la khang dinh dfldc. Do do, doi vdi bat ky mot ngon
ngfl khong khang dinh duoc, hocic no hoac phan bu cua no phai l a
khong doan nhan dugc. Theo dinh nghia, phan hu (complement) ciia ngon ngfl // trgn bang chfl E la ngon ngfl gom t a t ca nhflng t f l trong S* ma khong thuoc L, va dugc ky hieu bdi / / .
D i n h ly 1.4.6 Mot ngon ngu Id khdng dinh duac neu va chi neu no vd ca phan bu cua no deu Id doan nhan duac.
Chiing minh Dau tien, gia sii L l a ngon ngfl khang dinh dugc bdi •^ay Turing dflng M. K h i do L hign nhign la doan nhan dugc va
phan bu cua no / / doan nhan dugc bdi may Turing A/'', trong do ^Z" thu dugc t f l A/ b&ng each hoan đi vai tro cua hai trang thai
9 8 May Turing va Thuat toan "chap nhan" va "bac bo". Chinh xac hon, moi ngon ngfl khang dinh "chap nhan" va "bac bo". Chinh xac hon, moi ngon ngfl khang dinh duac deu la doan nhan duoc, va phan bh cua moi ngon ngu: khang dinh duoc cung la khang dinh duoc.
Nguoc lai, do L va deu la doan nhan d U d c . Gia sit Mi \h mAy
Turing doan nhan L va A/2 la may Turing doan nhan L'^. K h i do may Turing sau day quyet dinh ngon ngu: L .
M = " T r e n til vao w: