Body: <p>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</p>
  <p>L1/L2 = {x : xy ∈ L1 for some y ∈ L2}.</p>
  <p>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?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-09-29T16:22:57.417Z
Comments.Text: 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.
Comments.UserDisplayName: Buffy
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-09-29T18:49:43.713Z
Comments.Text: @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.
Comments.UserDisplayName: vonbrand
Tags: <cs-theory>
Title: What are the real-life use cases for for fractional/quotient regular languages?
ThreadText: # What are the real-life use cases for for fractional/quotient regular languages?
  
  (Asked by: username_0 on 2021-09-29)
  
  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?
  
  **Tags:** cs-theory
  
  > **Comments:**
  > **username_1**: 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.  
  > **username_2**: @username_1, 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.  
  
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  ## 0 answers
  
  