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Today someone created the tag [recurrence-relation], which seems to me to cover the same ground as the already-existing tag [recursive]. I'm tempted to replace [recurrence-relation] with [recursive] in that question, which would cause the former to disappear as a tag.

However, I think [recurrence-relation] is a better tag than [recursive] for questions on this topic. I've never liked [recursive] as a tag, actually. I think my problem with it is aesthetic: Our tags tend to be nouns, and this is one of the few (the only?) that is an adjective. So I'm also tempted to request that [recursive] be merged into [recurrence-relation].

Since I have two different thoughts on this, I thought I would see if anybody in the community has strong feelings one way or the other.

(For the record, the question is Common Term for Differential Equations and Recurrence Relations.)

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    $\begingroup$ I'm entirely in favor of merging the [recursive] tag into [recurrence-relation] or maybe even better [recursion]. The [recursive] tag looks strange and I strongly suspect that it is a stub left over from tagging a question e.g. by "recursive definition" without a dash. This tag was at least mentioned twice already in the merging and synonyms thread namely here and here (look at the comments there as well). $\endgroup$ – t.b. Jun 3 '11 at 0:24
  • $\begingroup$ @Theo: Thanks. I missed those prior conversations - should have looked at the "tag merging and synonyms" question. Given Aryabhatta's answer below and comments on the links you provided I think someone will have to go through the [recursive] tag manually and change some over to [recurrence-relations]. $\endgroup$ – Mike Spivey Jun 3 '11 at 3:01
  • $\begingroup$ Isn't this like combining "derivative" and "differential equation"? $\endgroup$ – GEdgar Jun 3 '11 at 13:58
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    $\begingroup$ recursive should be a synonym for recursive. $\endgroup$ – kinokijuf Dec 25 '11 at 13:39
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The "recursive" tag never seemed to be very informative to me: it had recurrence relations, computable functions, transfinite recursion, and who knows what else.

I would suggest:

  • Computability questions should be tagged "computability", which is already merged with "recursion-theory"
  • Questions about recurrence relations should be tagged as "recurrence-relations"
  • Questions about transfinite recursion should be tagged "transfinite-recursion". This could be achieved by renaming the "recursive-mappings" tag to "transfinite-recursion", which doesn't exist at the moment.
  • The "recursive-algorithms" tag be left for questions about actual algorithms (not just about computable functions in general)
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  • $\begingroup$ I agree completely with Carl's suggestion. $\endgroup$ – JDH Jun 6 '11 at 2:28
  • $\begingroup$ I second Carl and JDH. $\endgroup$ – Yuval Filmus Jun 6 '11 at 2:57
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    $\begingroup$ I concur with Carl and JDH and Yuval. $\endgroup$ – Asaf Karagila Jun 6 '11 at 7:58
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As far as the uses in logic are concerned, I fear that many of the tags previously and after the current major changes are all slightly off-sounding. In logic we have recursion and definitions by recursion and transfinite recursion, and there is the subject formerly known for decades as recursion theory (but which actually had little to do with actual recursive definitions) and is now known as computability theory. Thus, many uses of the word "recursive" in logic have to do with computability rather than actual recursions. I almost never hear the terms "recursive mappings" or "recurrence relations" in areas of logic itself. Many of the recently re-tagged questions in logic concerning recursion seem off to me, and I would suggest that we relax for the moment about further re-tagging until a greater agreement is attained.

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I would say we leave the tags as they are don't merge them.

In computer science, recursive can mean a specific class of languages. A recursive algorithm need have any involvement with a recurrence relation.

Basically, I don't think the tags are equivalent enough...

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    $\begingroup$ Why not then add tags (recursive-language) and (recursive-algorithm)? $\endgroup$ – Yuval Filmus Jun 3 '11 at 2:53
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    $\begingroup$ Hmmm... didn't think of that. Maybe someone will have to go through the [recursive] tag manually and switch some over to [recurrence relations]. $\endgroup$ – Mike Spivey Jun 3 '11 at 3:03
  • $\begingroup$ @Yuval: We could, but too fine grained tagging could lead to the tags becoming useless. In this case, though, what you suggest is perfectly fine. $\endgroup$ – Aryabhata Jun 3 '11 at 3:10
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    $\begingroup$ There's also the tag (computability) which is pretty much the same as (recursion-theory). $\endgroup$ – Yuval Filmus Jun 3 '11 at 4:32
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    $\begingroup$ @Yuval: Thanks for doing what I suggested. We might want to do only a few at a time, though, so that the front page isn't completely overwhelmed with the retagged old questions. $\endgroup$ – Mike Spivey Jun 3 '11 at 4:33
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    $\begingroup$ If we do it "a few at a time" I'm afraid it won't happen. It's a pity we can't disable the bumping. $\endgroup$ – Yuval Filmus Jun 3 '11 at 4:45
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    $\begingroup$ One more problem: set-theoretic recursion, which I'm also tagging as (recurrence-relations). $\endgroup$ – Yuval Filmus Jun 3 '11 at 4:45
  • $\begingroup$ @Mike: On the other hand, this means less work for me! So I gladly accept. Someone else will have to do the rest, little by little. $\endgroup$ – Yuval Filmus Jun 3 '11 at 4:51
  • $\begingroup$ @Yuval: It is indeed a pity. $\endgroup$ – Asaf Karagila Jun 3 '11 at 5:32
  • $\begingroup$ I added one more, the badly named (recursive-mappings), for the set theory stuff. Maybe it should be renamed to (transfinite-recursion) or something. The tags don't cover recursively-defined functions (e.g. Ackermann), but there was only one such question so I just dropped "recursive". $\endgroup$ – Yuval Filmus Jun 3 '11 at 20:17

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