M khong vuot qua so tat cacac hinh thai khac nhau Ct = UtqiVt
2. Khii > 1, doi vdi tiitng hinh thai Ck cua  trgn w:
2ạ Tinh gia tri REACHABLE(C, Ck,j - 1).
2b. Tinh gia tri REACHABLE(Cfc, C\j - 1).
2c. Neu ca hai gia tri thu dUdc d cac budc trgn day deu la
DUNG, thi REACHABLE(C, C\j) = DUNG.
2d. Neu dgn cung, khi khong c6 mot hinh thai nao
ma ca hai gia tri thu dupe ay deu la DUNG, thi
REACHABLE(C, C\j) = SAL"
Bay gid, đ mo phong may Turing N, ta xay dung may Turing
tat dinh M nhu sau: M = "Trgn tit vao w:
1. Tinh gia tri R-Ekc\iABLE{qQW,q^(2),cs{n)). Neu ket qua thu dudc la DUNG, thi chap nhm; nguoc lai, bdc bọ" thu dudc la DUNG, thi chap nhm; nguoc lai, bdc bọ"
Cuoi Cling, ta c6n phai danh gia khoang khong gian ma may M ckn sijf dung trong qua trinh tinh toan. Ro rang, so tang de quy la
0[s{n)] va tai mOi tang de quy, vdi gia thiet s{n) > logn, khoang
khdng gian can thigt dg liiu trfl cac hinh thai C, C \k Ck \k 0[s{n)
(theo nhan xet ngay sau Dinh nghia 3.1.6). Do vay, may M cin sii dung mot khoang khong gian tinh to^n la 0\s^[n)
Dinh ly dUdc chiJng minh.
3.3 Do phiJc tap khong gian da thufc
Nhu da thdy, nghien ciJu do phiic tap thdi gian da thilc c6 y nghia quan trpng ca ve ly thuyet Itn thuc tien. Bay gid ta hay trign khai "^hiing nghign ciiu ve do phiic tap khong gian da thiic, b^t dau
^ỉc dinh nghia cac Idp phiic tap dfe vi$c khao sat tinh d^y dii cua
230 Do phiic tap khong gian
3.3.1 Cac Idp phu-c tap PS va NPS
Tudng tir nhu cac Idp pMc tap P va N P , doi vdi do phiic tap khong gian da thiic, ta c6 cac Idp P S va N P S tirong ling.
Dinh nghia 3.3.1 Cac Idp pMc tap P S va N P S duac xdc dinh nhu sau:
P S la Idp tat ca cac ngon ngU duac khdng dinh bdi may Turing tat dinh khdng gian da thiic. Noi each khac,
P S = U SpACE(n'=).
k
N P S la Idp tat ca cac ngon ngU duac khdng dinh bdi may Turing • khdng tat dinh khdng gian da thvtc. Ndi each khac,
N P S = U NSpACE(n'=). •
k
Ve tuong quan giuia cac Idp phiic tap P va N P ta da biet rkng,
P = N P la mot van dg hoc buạ Tuy nhien, doi vdi cac Idp P S va
NPS, van de lai kha don gian. Theo dinh nghia, P S C N P S . Con bao ham thirc N P S C P S duoc suy ra true tiep tif Dinh ly Savitch, bdi V I binh phudng cua da thutc cung la da thiic. Nhu vay, hai Idp phiic tap P S va N P S trung nhaụ
He qua 3.3.2
P S = N P S , •
Bay gid ta hay khao sat moi quan he gifla Idp P S vdi cac Idp phutc tap quan trong khac nhu nhflng Idp P, NP, N P S va E , trong do E = Ufc TIME(2"'). Trudc tien, theo He qua 3.2.3 (i), Idp N P S
chiita Idp N P va do P S = N P S , Idp P S chiia Idp N P va dudng nhien chiia ca Idp P. Tiep theo, t i l He qua 3.2.3 (ii) suy ra r^ng Idp
P S va roi ca Idp N P S cung thuOc Idp Ẹ
3.3 Do phUc tap khdng gian da thitc 231
Hinh 3.1 Cac moi quan he gia dinh giiia nhiJng Idp phirc tap P, NP, P S va E
Hinh ve 3.1 mieu ta cac moi quan hg giiia nhilng Idp philc tap quan trong. Trong s6 cac moi quan he do ta chi duqc biet rang
PS = N P S . Bang each thg hien khac, quan he giiia nhiing Idp phiic tap nay c6 the dudc dign ta bdi mot day cac bao ham thiic sau day:
P C N P C P S = N P S C Ẹ
Cho dgn nay ta chua biet dUdc bao ham thiic nao trong so nhiing bao ham thiic neu trgn la chat hoac la dang thiic, ngoai t r i i d i n g thirc P S = N P S dildc xAc lap nhd Dinh ly Savitch. Tuy vay, trong Chudng 4 ta se chiing to r^ng P 7^ Ẹ V i the, it nhat mot bao ham thiic nao do trong s6 ay phai la chat, nhung cu thg bao ham thiic fiao thi ta khong thg chi ra dUdc. Hien nay da phan nhiing ngudi quan tam den llnh vuc nghign ciiu nay cho r^ng, tat ca nhiing bao ham thiic neu tren deu la chat.