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Definition of NP-hard
1. 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. ¹
2. Adjective. (computing theory) An alternative definition restricts NP-hard to decision problems and then uses polynomial-time many-one reduction instead of Turing reduction. ¹
¹ Source: wiktionary.com