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Under the assumption that P would be equal to NP, it could exist a NP-complete problem that is solved in constant time?

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  • $\begingroup$ What have you tried? Where did you get stuck? We do not want to just hand you the solution; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for tips on asking questions about exercise problems. If you are uncertain how to improve your question, why not ask around in Computer Science Chat? $\endgroup$ – Raphael Apr 16 '17 at 18:32
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Write down the definition of NP-complete. Then take your assumption that P = NP, so in the definition of NP-completeness you can replace "NP" with "P". Figure out which functions exactly are NP-complete. (Hint: There is a simple and obvious solution that is almost but not quite correct. Read the definition carefully). Do these functions contain any constant time solvable problems?

Each step is actually quite simple, you just have to follow all the definitions very precisely.

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