if l1 is in NP-HARD
, so for every L2!=empty set, l1*l2 is in np-hard
.
when:
l1*l2={(w1,w2) , w1 in L1 and w2 in L2}
Is it true or false and why?
I can't approve it but I also don't find counter example.
if l1 is in NP-HARD
, so for every L2!=empty set, l1*l2 is in np-hard
.
when:
l1*l2={(w1,w2) , w1 in L1 and w2 in L2}
Is it true or false and why?
I can't approve it but I also don't find counter example.
L1 * L2 is NP-hard.
Proof: Let L be a language in NP, let f be a reduction of L to L1 and let w2 be in L2. Define g(x) = (f(x), w2). Now g is a polynomial time many-to-one reduction of L to L1*L2 because clearly:
x in L <==> (f(x), w(2)) in L1*L2