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I had a paper accepted in a workshop that only publishes its proceedings on its website; one of these workshops that tell you that submitting to the workshop does not prevent you from submitting elsewhere. The paper proposed a new method A, and applied it to problems B and C.

Now, I want to write a conference version of the paper. The conference version will present method A, apply it to problems B and C with extended experiments, and additionally to problem D.

How do I refer/cite the method A in the conference paper? Does the workshop count at all? In my field (CS), I have been told that the workshops do not count. Yet, it feels wrong to call it a novel method. Is the method A contribution of the conference paper or not?

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I think you are mixing up a few different definitions of "count" here.

  1. Workshop papers typically "count" very little on your CV. That is, having a few workshop papers will not make you graduate much sooner, and they are pretty much useless when you start looking for e.g., a tenure track position.
  2. Workshop papers, but only those with no formal proceedings, don't "count" as publications. That is, you can hand in the same material again at a conference or journal without being accused of self-plagiarism. The workshop paper on the website of the workshop is basically a preprint. Hence, formally, the work is still unpublished and you can submit it wherever you want.
  3. Workshop papers, no matter if they appeared in formal proceedings or not, can and should be cited. Clearly, if you use this citation to, e.g., support the validity of a statement, this carries less weight if the cited source is a workshop paper than if it is a well-known journal. However, if you want to apply method A, which you have already presented in a workshop, it seems correct to cite the workshop paper. Note that you will still need to describe the method, as you cannot assume the reader of your conference paper to go back and read the workshop paper first.

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