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Avoiding the trivial certificate in complexity class NP

Discussion in 'Computer Science' started by Shuheng Zheng, Oct 8, 2018.

  1. One definition of the class NP is that there is a certificate whose size is bounded by a polynomial function of the problem instance size which can be used on a deterministic TM, along with the original input, to decide whether the input is a part of the language.

    Doesn't this definition allow the trivial loophole where we let the certificate simply be 1 if the input is a part of the language and 0 otherwise? Then the deterministic just uses the certificate entirely and totally ignores the input.

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