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In computer science theory some textbooks introduce fractional/quotient regular languages. In particular, given L1 and L2 languages on the same alphabet, the right quotient of L1 with L2 is defined as

L1/L2 = {x : xy ∈ L1 for some y ∈ L2}.

The left quotient is defined in a similar way. I was wondering if there are some real-life cases in which quotient languages can be useful. Any ideas?

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    $\begingroup$ Do you mean " L1 and L2 are regular languages on the same alphabet". I haven't seen the concept before. Which textbook(s). Hopefully plural. I'd expect the book author(s) to give some reasonable examples. $\endgroup$
    – Buffy
    Sep 29 at 16:22
  • $\begingroup$ @Buffy, the definition makes sense for all languages, not just regular ones. And proving that such constructions give regular languages if $L1$ and $L2$ are regular is a popular exercise. $\endgroup$
    – vonbrand
    Sep 29 at 18:49

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