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P, NP, NP-hard

P, NP, NP-hard. P, NP, NP-hard diagram. NP. NP-hard. P. NP-complete. P, NP problems definitions. P = {L І з p(n), M (deterministic) solves L in p(n) time} NP = {L І з p(n), M (non-deterministic) solves L in p(n) time}. NP-hard, NP-complete problems definitions.

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P, NP, NP-hard

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  1. P, NP, NP-hard

  2. P, NP, NP-hard diagram NP NP-hard P NP-complete

  3. P, NP problems definitions • P = {L Ізp(n), M (deterministic) solves L in p(n) time} • NP = {L Ізp(n), M (non-deterministic) solves L in p(n) time}

  4. NP-hard, NP-complete problems definitions • L is NP-hard iffV Lx € NP: Lx ≤p L • L is NP-complete iff is NP-hard AND L € NP

  5. Demonstration • L1 ≤p L2 • L2 € NP • L1 is NP-hard => V Lx € NP: Lx ≤p L1 => Lx ≤p L2 => L2 is NP-hard NP-hard NP L1 P L2 NP-complete

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