M khong vuot qua so tat cacac hinh thai khac nhau Ct = UtqiVt
b. Hay danh gia do philc tap thdi gian cua may Turing vd
bang chuyen doc B^^\c xay dung trong V i du 3.1.4,
vk so sanh vdi may M naỵ
3.3 Chiing to rkng, doi vdi moi ham / : N ma f{n) > n,
iap"phirc tap SPACE(/(n)) khong thay d6i khi ta dinh nghia
16p ay bai mo hinh may Turing mot bang hoac bdi mo hinh , may Turing vdi bang chuyen doc.
3.4 Hay chiing to r^ng Idp P S dong kin doi vdi phep hdp phep
lay phan bụ
3.5 Hay chiing to rling Idp N L S dong kin doi vdi phep hop va
phep gh6p.
3.6 Chirng minh rang moi ngon ngu: PS-kho deu la NP-khọ 3.7 Hay chilng to vKng, neu m6i ngon ngO NP-kho cung la PS-kho 3.7 Hay chilng to vKng, neu m6i ngon ngO NP-kho cung la PS-kho
thi N P = PS.
3.8 Giasii
MULT = { x t i y p I x,y,'z\h bieu di§n nhi phan ciia
cac so til nhien x,y,z mk xy = z}. | Chilng minh r^ng MULT e L S .
Bai tap 257
3.9 ạ Gia sil
AĐ = { x t t y p I X, y, z la cac bilu dign nhi phan ciia
cac so tu nhien x,y,z mh x + y = z}. Chilng minh r^ng AĐ e L S .
b. Giasii
PAL-AĐ = { xtJy I x,y la cac bilu dign nhi
phan cua nhflng so tu nhien
x,y ma x + y Ih can xilng }. (Til w duoc goi la can xUng hay diep tic (palindrome)
n6u no trung vdi nguoc cua chinh no, tilc w = w'^.) Chilng minh r^ng PAL-AĐ e L S .
3.10 Ta dinh nghia
CYCLE = {(G) I G la do thi v6 hirdng chila chu trinh}.
Chilng minh rang CYCLE e L S .
3.11 Mot do thi vo hudng duoc goi la hai phdn (bipartite) neu
tap dinh cua no c6 the duoc chia thanh hai tap sao cho moi canh CO mot dau miit trong tap no va mot dau mut trong tap kiạ Hay chiir\ to rang, mot do thi la hai phan khi va chi khi no khong chiia chu trinh vdi do dai lẹ Gia sijf
BIPARTITE = {{G)\la do thi hai phan}.
Chirng minh rkng BIPARTITE e NhS.
3.12 Gia sil PATH\h ngon ngfl tuong ilng vdi ngdn ngO DIPATH,
duoc dinh nghia cho cac do thi vo hudng. Chilng minh r^ng
BIPARTITE PATH. (0. Reingold [27] thong bao r^ng PATH e L S . Vay la BIPARTITE e L S , the nhung thuat
258 Do phiic tap khong gian
3.13 Mot do thi c6 hudng duoc goi 1^ lien thong manh {strongly
connected) neu moi cSp dinh cua no diioc noi lien nhau b5i
c^c diidng di c6 hirdng theo ttog chieu mot. Gia sOf
STRONGLY-CONNECTED = {(G) | G la do thi lien
thong manh }.
Chiing to r^ng STRONGLY-CONNECTED la NLS-day dụ
3.14 GiasiJt
DICYCLE = {(G) I G la do thi c6 hudng chiJa chu trinh c6 htrdng •.
Chiing minh rang DICYCLE la NLS-day dụ
3.15 Chutng minh rang g-5Aria NLS-day dụ
1^