File talk:P np np-complete np-hard.svg

The right diagram is wrong. If P = NP, P is not equal to NP-complete. That is because the trivial decision problems (the problem that always returns true, and the problem that always returns false; i.e. problems that emit no information) are obviously in P but are not reducible from any problems that may return both true and false (I am assuming many-one reduction here). Thus, they are not in NP-hard, and thus not in NP-complete. --208.80.119.68 22:41, 22 February 2012 (UTC)

Please continue the discussion on the English Wikipedia talk page at https://en.wikipedia.org/wiki/File_talk:P_np_np-complete_np-hard.svg . Thanks, Behnam (talk) 21:36, 22 July 2012 (UTC)

Updated diagram to version 3

In the update to version 3, I'm now using "≃" for the relationship between P/NP and NP-Complete, to demonstrate approximate equality, as NP-Complete actually misses two members in its class, by definition, and therefore is not an exact equivalence to the other two. Thanks everyone for the feedback about this! Behnam (トーク) 03:50, 1 January 2020 (UTC)