D CO thg mo phon gM trong khong gian dg{n) vdi mot h^ng so
b.Chiing minh ran gP SpACE(n).
294 T i n h nan giai
4.10 Bai toan thoa dxidc duy nhat {unique-satisfiability) diioc
tuong ling vdi ngon ngu:
USAT= {(0) I 0 la cong thiic Boole thoa duoc bdi duy nhat mot phep gan t r i }.
Chuing m i n h rang USATeP^^^.
4.11 Chiing m i n h rang ton tai t\l vkn C sao cho N P ^ 7^ c o - N P ^ . 4.12 May Turing vdi ttC vdn k thac m&c, hay may Turing 4.12 May Turing vdi ttC vdn k thac m&c, hay may Turing
vdi k-tii van {k-orade Turing machine), la may Turing vdi
tir van chi giai dap nhieu nhat k thac mac tren tCrng dau vaọ Mdy Turing M vdi k-t\l vkn vg ngon ngfl A diioc ky hieu
\h M'^''^. Gia sit P^'*^ la Idp cac ngon ngfl diTdc khang dinh
bdi cac may Turing thdi gian da thilc vdi A;-tir van Ạ
ạ Chiing minh rang N P U c o - N P C pSAT,i_
b. Gia thigt rang N P ^ c o - N P . Hay chiing m i n h r^ng P U c o - N P C P ^ ^ ^ ' i . P U c o - N P C P ^ ^ ^ ' i .
4.13 Ta CO thg xay dirng mach vdi nhieu cong ra dg cho ket qua
t i n h toan la mot xau nao d6 tren bang chil {0,1}. Gia sut
aĐ n •• {0,1}^" —> { 0 , 1 } " + ! la ham cong hai so t u nhien dudi dang n h i phan vdi n bit va cho ket qua vdi n + 1 b i t . Chiing
minh r^ng ham a5D „ c6 thg tinh diioc bdi mach rong 0[n .
4.14 Ta dinh nghia ham troi majoritr)n: { 0 , 1 } " — > {0,1} nhiisau:
I I , neu 2^Xi> /i/2. Chiing m i n h rang hkm majoritt) „ c6 thg t m h duoc bdi: Chiing m i n h rang hkm majoritt) „ c6 thg t m h duoc bdi:
ạ Mach rong 0[n^]. \