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Wikipedia says, the regular languages are closed under

arbitrary finite state transductions, like quotient K / L with a regular language.

I wonder what kinds of operations "finite state transductions" are? Btw, It links to finite state transducer, an automaton. Thanks.

Raphael
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Tim
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    Finite state transductions are operations performed by finite state transducers, which are described in the link from the phrase "finite state transductions" in the Wikipedia article. Pleaee ask a more specific question about the parts you didn't understand. – David Richerby Jun 01 '14 at 20:48
  • Yes, I read. But there is no "transduction" mentioned in the Wikipedia article for finite state transducer. (1) did you mean that the operation of "a finite state transduction" is defined as, applying its operand string to a "finite state transducer", and then taking the output of the "finite state transducer" on the operand string as the return by the operation of "a finite state transduction"? (2) Will the operation of "a finite state transduction" be different for different finite state transducers? – Tim Jun 01 '14 at 21:35
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    "On this view, a transducer is said to transduce"; "transduction" is the act of transducing. (1) Yes, and this is applied to whole languages: you start with a language $L$, feed every string of it to your transducer and the set of outputs you get is a new language. (2) Of course, just as the operation of "finite state acceptance" is different for different automata. – David Richerby Jun 01 '14 at 21:43
  • Can a "finite state transduction" be equivalent to some combination of more usual operations? – Tim Jun 01 '14 at 21:45
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  • Please take more care with your question, to state the question precisely. Provide all relevant information. In this case, if you had written "I understand what a finite-state transducer is, but what is a transduction?", that would have helped. 2. When people offer comments or it becomes evident that your question was unclear, please edit your question to improve it. Don't just drop answers in the comment thread. The question needs to stand on its own, without reading the comments. Comments exist only to help you improve the question. 3. One question per question, please.
    • – D.W. Jun 02 '14 at 06:01
  • @D.W.: Dear D.W. (1) I don't understand how adding "I understand what a finite-state transducer is, but what is a transduction?" will help make my question precisely. (2) I don't agree that my question can't stand alone. (3) My questions in the post and comments are closely related, and I have only one question in the post by far. I don't know why you could ask more than one question, e.g. here, while you insisted that others couldn't. – Tim Jun 02 '14 at 13:49
  • Well, two readers had to ask clarification questions to understand what you want to know, so that is empirical evidence that your question does not stand on its own in its current form. I'm trying to help you understand how this site works: when someone asks you a question in the comment threads, we ask you to edit the question to add enough clarifications to the question itself that others will be able to understand, without having to read the comment thread. If you want to deviate from these expectations, that is your choice, but it may lead to your post being closed. – D.W. Jun 02 '14 at 18:30
  • @J.-E.Pin, I hear you. If you'd like to keep the question open, you are always free to click the edit button to suggest an edit to make it a clear, well-posed technical question that everyone can understand and that you can answer. It's not your obligation to do that, of course, but it is an option available to you if you would like. Or, you could post a new question and answer it yourself, if you choose. – D.W. Jun 02 '14 at 18:33
  • I don't frequently override the community on matters of moderation, but I see no reason why this question should have been closed. It's completely clear and answerable. The question even shows some research effort. Please down vote to express dislike/disapproval of a question. I will clean up some of the comments here which are no longer relevant. – Patrick87 Jun 04 '14 at 14:30
  • @Patrick87, I think the comments explain the reasons for the close votes. As David Richerby says, "Please ask a more specific question about the parts you didn't understand.". The author had multiple opportunities to edit the question to clarify exactly what he is asking, and declined to do so. I still find it unclear what this is asking. Either it is asking us to regurgitate Wikipedia and standard textbooks (in which case the question is not a good fit) or it is not clear what the author doesn't understand / is looking for. Just my view. – D.W. Jun 04 '14 at 17:31