Adjective
(computing theory) A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H.
(computing theory) An alternative definition restricts NP-hard to decision problems and then uses polynomial-time many-one reduction instead of Turing reduction.
Source: en.wiktionary.orgAlthough it is widely suspected that there are no polynomial-time algorithms for NP-hard problems, this has never been proven. Source: Internet
Consequences * If P ≠ NP, then NP-hard problems cannot be solved in polynomial time; * If an optimization problem H has an NP-complete decision version L, then H is NP-hard. Source: Internet
It is easy to prove that the halting problem is NP-hard but not NP-complete. Source: Internet
;NP-hard: Class of problems which are at least as hard as the hardest problems in NP. Source: Internet
NP-hard problems are those at least as hard as NP problems, i.e., all NP problems can be reduced (in polynomial time) to them. Source: Internet
NP-hard problems need not be in NP, i.e., they need not have solutions verifiable in polynomial time. Source: Internet