D CO thg mo phon gM trong khong gian dg{n) vdi mot h^ng so
272 Tinhna ngia
T h i du, gia s i i Aug ta ban cho m^y Turing kha nSng giai bai
toan thoa duac chi b^ing mOt phep bien dSi dan gian, doi vdi bat ky mot cong thilc Boolẹ Diitng ban tarn den su t h k n h thao cua ky cong nky, ma hay hinh dung day nhu mot "hop den" duoc g^n kgt d i tao
cho may kha nSng n h u vaỵ Ta goi hop den ay la bp phan tii vdn, hay dung hon la bo phan "tien trí\ nhan manh r^ng no khong
h i n tuong ling vdi bat cii thiet bi vat ly naọ Ta dung thuat ngti "tien t r i " ("oracle") vdi ham y ve kha nang bien dQi than thong cua bo phan naỵ R6 rang may Turing c6 thg sii dung bo phan t u van ve
bai toan thoa duoc dg giai bat ky bai toan cua Idp N P trong thdi gian da thiic, khong can quan t a m lieu P c6 b^ng N P hay khong,
bdi VI moi bai toan cua N P deu quy dan thdi gian da thiic den bai
toan thoa diioc. May Turing hoan thanh duoc nhflng t i n h toan nhu
vay la nhd tao duac moi quan he gifla may va bo phan t u van ve bai toan thoa dugc, do do thuat ngu: "quan he hoa" {relativization)
duoc siJt dung d daỵ
Noi chung, bo phan t u van c6 the cung cap thong t i n ve bat cii ngon ngu: nao khac, khong nhat thiet ve bai to6n thoa duoc. Han niJa, khong chi may Turing tat dinh sii dung bo phan t U van de thu thap thong t i n ma may Turing khong tat dinh cung c6 thg sii dung dich vu naỵ Bo phan t U van cho phep may Turing xac dinh t U each thanh vien cua ngon ngu nhung thuc sir khong phai t i n h toan.
Ta hinh thufc hoa khai niem nay mot each ngan gon nhu saụ
D i n h n g h i a 4 . 2. 1 Bg phan ttC vdn {oracle) ve ngon ngU B la
mot thiSt bi ngoai vi c6 kha nang thong bdo "lieu mot tic bat ky w c6 la thanh vien cua B hay khong". May Turing vdi tx£ van {oracle
Turing machine) la may Turing duac chinh sxia sao cho no c6 kha
nang chat vdn bo phan tU vdn duac gan kit. Ta viet de biiu thi may Turing vdi bo phan tU vdn ve ngon ngU B. Mdi khi mgt tii dudc ^ ghi tren bang tU van rieng biet, may duac thong bdo rang ti^
dy thuoc B hay khong thuoc, chi sau mot phep bien dSi dan gian. ^
Phuang phdp quan he hoa vd vdn de P= NP 273
R6 rang, may Turing vdi t u van c6 thg khang dinh duoc nhi^u ngon ngu: han so vdi may Turing thong thudng.
V i d u 4 . 2. 1 Ta xem xet t u van vg Aru- May Turing vdi bo phan t u van ve ngon ngu Aru c6 thg khang dinh chinh ATM, hKng each chat van bo phan t u v4n ve dau vao {Af,w). Hay nhd r^ng ATM
la ngon ngij tuang ling vdi bai toan chap nhan ma ta da xem xet trong Muc 1.4.1 va la ngon ngu khong khang dinh duac bdi may Turing thong thudng. Gia sijt
ETU = {{M)\M\h may T u r i n g ma L M = 0 }
la ngon ngfl tuang ling vdi bdi toan rdng {emptiness testing prob-
lem) doi vdi may Turing, tiic bai toan kigm t r a xem lieu ngon ngii LM cua may Turing M c6\h rdng hay khong. Co thg chirng to rang ETU la khong khang dinh duoc bdi may Turing thong thudng (Bai
tap 1.9). Tuy nhien, may Turing vdi bo phan t u vdn vg Âu, duac
ky hieu la T ^ T M ^ dinh Êu va duac mo ta n h u saụ
TATU ^ âi-en dau vao { M ) , trong d6 y\ la may Turing:
1 . Xay dung may Turing S sau daỵ
5 = " Trgn moi dau vao thuoc S*:
l a . Cho M tinh toan song song trgn tat ca cac
tiif thuoc E*.
l b . Neu M chap nhan bat cur mot t\l nao trong
so nhflng t\i ay, chap nhan."