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NP-complete and NP-hard problems. Transitivity of polynomial-time many-one reductions Definition of complexity class NP Nondeterministic computation Problems that can be verified The P = NP Question Concept of NP-hard and NP-complete problems. P 1 ≤ p P 2 & P 2 ≤ p P 3 P 1 ≤ p P 3.