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In a conference paper, in order to prove the $\mathsf{NP}$-completeness of a problem, I wrote the stupid sentence "It is clear that the problem is in $\mathsf{NP}$. So we will prove that it is $\mathsf{NP}$-hard". In fact, it was not clear at all. It even seems to be an open problem. For the targeted audience, it's not a big deal because the main result is the $\mathsf{NP}$-hardness, and thus the impossibility "difficulty" to design a polynomial algorithm.

But, of course, I want to correct the mistake in the journal version.

My question is: In a journal paper, how to point a mistake in the conference version and correct it?

Should I write: "There is a mistake in the conference version: ..."? Or should I state the correct result without saying that the conference version was wrong? Any advise is welcome.

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    $\begingroup$ In addition to correcting the mistake in the journal version, I think it is helpful to post the postprint version of the paper in a repository (e.g., arXiv) with the corrected statement and indication that the publisher version contains an error. (If the paper has already been deposited, you can update the deposit to do this.) $\endgroup$
    – a3nm
    Apr 24, 2017 at 17:08

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I think it is very helpful to point out if and where previous results are erroneous. I've done this myself (more times than I would have liked to). My style is to state the correct result, and in immediate proximity (above, below, footnote) a remark to the effect that "In the conference version [citation], Theorem X incorrectly stated that...".

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  • $\begingroup$ Thank you. Do you think that it's also relevant to point the problem in the cover letter? $\endgroup$
    – Lamine
    Apr 26, 2017 at 7:35
  • $\begingroup$ I don't think that's necessary, but I don't see the harm. "Along the way, this manuscript corrects an error in one of the claims in the extended abstract..." $\endgroup$
    – Aryeh
    Apr 26, 2017 at 8:09

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