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Poly Time Mapping Reducibility
Poly Time Mapping
Reducibility
•
••
P NP
• P•
• NP•
• P = NP•
•
P = NP
•
•• NP
^ ^
P
P
^ ^
^
^
O(k)
O(k2)
TRUE FALSE ( 1 0) TRUE, FALSE
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
•
• TRUE FALSE 1 0TRUE
••
• x = 0, y = 1, z = 0
SAT NP:
• n
•• c• O(n)
••
• O(n)
• 3SAT
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
OR
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
OR
AND
TRUE FALSE ( 1 0) TRUE, FALSE
x, y, z
AND, OR, NOT ( )
OR
AND
3SAT
•••
••
• TRUE•• x1 = 0, x2 = 1
<= f( ) CLIQUE ••
O(k)
O(k2)
• CLIQUE NP 3SAT NP
NP
• P = NP NP
NP
NP
Check-in Quiz 4/28
