M CO diTng hay khong tren w la yeu to quyet dinh su ton tai thuat
92May Turing va Thuat toan n fin)
n fin) 1 1 , 0 0 0 0 0 . . . 2 3 , 1 4 1 5 9 . . . 3 5 5 , 5 5 5 5 5 . . . 4 0 , 1 2 3 4 5 . . . •
Ro rang, doi v6i moi n, cac so x va / ( n ) khac nhau bdi v i thanh
phan thap phan thut n cua chung khac nhaụ • Dinh ly vHa dUdc chiing minh c6 utng dung quan trong trong ly
thuyet tinh toan. No giup ta chiing to rang ton tai nhflng ngon ngii khong khang dinh dudc hoac tham chi khong doan nhan diroc, bcii vi so cac ngon ngu: la khong dem diroc con so cAc may Turing la dem diroc, nghia la so cac ngon ngii nhieu hon so cac may Turing. Hon niia, m6i may Turing chi doan nhan mot ngon ngii va do do c6 cac ngon ngii khong dugc doan nhan bdi may Turing. Nhiing ngon ngii nhir vay la khong doan nhan daoc (theo Turing). Vay ta di den ket luan nhu saụ
He qua 1.4.5 Ton tai cac ngon ngii khong doan nhan duac.
ChUng minh Dg chiing to r^ng tap tat ca cac may Turing la dem duoc, dau tien ta nhan thay rang tap tat ca cac tit trong E* la dgm dugc, doi vdi mgi bang chii hiiu han Ẹ Sap xep tat ca cac t i i ciing do dai vdi so lugng hiiu han theo thii t u t i l d i i n chang han, ta c6
thi tao lap danh sach doi vdi E* b^ng each liet ke tat cac cac tit do dai 0, do dai 1, do dai 2, va v.v...
Tap tat ca cac may Turing la dem dugc bdi v i moi may Turing
M deu dugc ma hoa thanh mot t i l (A/). N i u don gian ta gat bo khoi danh sach E* nhiing t i l khong la ma hoa cua may Turing, ta
CO the thu dugc danh sach tat ca cac may Turing.
1.4 Mot vai bai toan khong gidi duac 93
Dg chiing to rang tap tat ca cac ngon ngU la khong d^m dugc, ta nhan thay r^ng tap tat ca cac day nhi phan v6 han la khong dem dugc. Day nhi phan v6 han la day dai v6 han bao gom cac ky tu 0 va 1. Gia sii B la tap tat ca cac day nhi phan v6 han. Ta c6 t h i chiing to rang B la khong dem dugc bang phugng phap dudng cheo tugng t u nhu ta da sii dung trong chiing minh Dinh ly 1.4.4
ve tinh khong dem dugc cua R.
Gia sii C tap tat ca cac ngon ngii trgn bang chu Ẹ Ta chiing to rang C la khong dem dugc b&ng each thiet lap phep tugng ling vdi B,
va do do hai tap nay c6 eiing luc lugng. Gia sii E* = { s i , S2, S 3 , . . . }
la danh sach cde t i l tren Ẹ Khi do m6i ngon ngii A e C tuong ling vdi duy nhat mot day trong B. Day nay duge xac dinh nhu sau: ky tu thii i la 1 neu 6 v4 va la 0 neu Sj ^ / I , va do do dugc ggi la day
d&c trung cua A . Thi du, neu cho A la ngon ngii gom tat ca cac t i l bat dau bdi 0 trgn bang chii {0,1}, day dac trung XA cua no se la
E* = { e , 0 , 1 , 00 , 01 , 10 , 11 , 000, 001, • • •} ;
A = { 0 , 00 , 01 , 000, O O l , - - - } ;
XA= ^ 1 0 1 1 0 0 1 I - - - .
Ham / : £ —> 5, trong do f{A) bang day dac trung cua A , la ham
mpt-mgt len va do do la mot phep tugng ling. Bdi vay, do B khong dem dugc nen C eiing khong dem dugc.
Nhu vay ta da chiing to rang tap tat ca cac ngon ngii khong the cho tuong ling vdi tap tat ca cac may Turing. Tren cd s6 nky ta ket luan rang tSn tai nhUng ngon ngii khong doan nhan dugc bdi bat
cii may Turing naọ •
• B a i toan chap nhan la khong giai difdc
gid ta c6 the chiing minh Dinh ly 1.4.1, tiic chiing minh tinh khdng khang dinh dugc eiia ngon ngU
94 May Turing va Thuat toan
CMng minh Gia thijt rSng ngon ngfl ATU la khang dinh duoc. TCf
gia thiet nay t a t i m cdch dan den dieu mau t h u l n . Gia sxi H la
m&y quyet dinh doi vdi ngon ngii ATM- K h i t i n h toan tren dau vao
{M,w), trong do M la may Turing va w la mot tit, may H dCtng (adsbygoogle = window.adsbygoogle || []).push({});
va chap nhan (accept) neu may M chap nhan w. Hon nfla, may H d t o g va bac bo (reject) ngu may M khong chap nhan w. N6i each khac, ta gia t h i i rang ton tai may Turing H ma tren moi dau vao
{M, w) cho ta ket qua t i n h toan:
{ accept neu Af chap nhan w,
reject neu M khong chap nhan w.
Bay gid, diia theo sir tinh toan cua may H, ta xay di/ng may Turing mdi C. May Turing mdi nay yeu cau H x4c dinh xem m5i may Turing M x i i ly the nao khi ma dau vao cua A/ la b i i u dign cua chinh no {M). M o t khi C c6 duoc thong t i n nay, no thirc hien nguac lai vdi H; nghia la no bac bo ngu M chip nhan va chap nhan neu M khong chap nhan. May C diioc m5 t a nhil saụ
C = "Tren dau vao (A/), trong do Af la may Turing: