I unable to understand polynomial reduction. Here is the definition :
"A problem L1 reduces to L2 if and only if there is a way to solve L1 by deterministic polynomial time algorithm using a deterministic algorithms that solves L2 in polynomial time"
Is this is correct ? If yes, I would appreciate if someone can explain it to me.
Next, NP Hard :
"A problem L is NP-Hard if and only if satisfiability reduces to L
i.e. SAT < L "
But shouldn't it be L < SAT ? i.e. Reducing L to satisfiability ? Since we reduce L to satisfiability and since satisfiability is a known NP - Complete according to Cook, therefore we can conclude L as a NP-Hard ?
I would appreciate if someone can provide me some examples.
Thank you !
"A problem L1 reduces to L2 if and only if there is a way to solve L1 by deterministic polynomial time algorithm using a deterministic algorithms that solves L2 in polynomial time"
Is this is correct ? If yes, I would appreciate if someone can explain it to me.
Next, NP Hard :
"A problem L is NP-Hard if and only if satisfiability reduces to L
i.e. SAT < L "
But shouldn't it be L < SAT ? i.e. Reducing L to satisfiability ? Since we reduce L to satisfiability and since satisfiability is a known NP - Complete according to Cook, therefore we can conclude L as a NP-Hard ?
I would appreciate if someone can provide me some examples.
Thank you !