May Turing duoc de xuat vao nam 1936, theo nhu cau dinh nghia chinh xac khai niem thuat toan ma trude do ehi duoc higu mdt each true giaẹ Vdi nguyen tac hoat dong kha don gian, may Turing khong ehi la mot khai niem chinh xac ve thuat toan duoc thiia nhan rong rai nhat, ma con la mo hinh kha diing d^n cua hau het moi qua trinh tinh toan. Ndi rieng, may Turing eung la mot mo hinh cua may tinh thuc te, ma nhd do mot trong nhflng may tinh tu dong dau tign duoc thiet ke va che tao thanh cong.
NOi dung chinh ciia chuong nay la gidi thieu ba dang cO ban eiia may Turing (may Turing tat dinh mot bang, may Turing tat dinh nhieu bang va may Turing khong tat dinh) va chiing minh su tuong duong giua ehung. May Turing con duoc chiing minh la tuong duong vdi nhung mo hinh tinh toan khae duoc de xuat cho khai niem thuat toan. Digu do t h i hien kha nSng tinh toan to Idn
cua may Turing mot bang va ly giai vi sao may Turing duoc lua
chon dg dinh nghIa khai niem thuat toan.
Dii kha nang tinh toan eiia may Turing la rat to Idn nhung no cung ed gidi han, do ed nhiJng bai toan khong thg giai duoc b^ng may Turing. Day lai la mot dieu thu vi theo nghia rat thuc tẹ No cho ta mot gidi han ve mat ly thuygt doi vdi tinh toan ndi ehung hay mdt ranh gidi giiia giai duoc va khong giai dudc doi vdi bai toan.
36 May Turing va Thuat toan
1.1 May Turing
1.1.1 M6 ta
• C a u t a o . May Turing {Turing machine), hay may Turing
tdt dinh mot bang đn {single-tape deterministic Turing ma-
chine), la mot mo hinh xii ly t i n t u dong, ma m6i du: lieu dau vao
duoc bigu di6n dudi dang mot tir tren bang chfl E nao dọ Qua trinh
hoat dong cua may di6n ra trong thdi gian rdi rac t = 0 , 1 , 2 , . . .
May bao gom mot bo phan dieu khign, mot bang vo han ve phia phai, va mOt dau doc-ghi ket noi bo phan dieu khien vdi bang.
Dau doc-ghi
0 0 0 0 1
Bo phan digu khign
H i n h 1.1 So do may Turing