<p>The <a href="https://en.wikipedia.org/wiki/Regular_tree_grammar" rel="nofollow noreferrer">Wikipedia page for Regular Tree Grammars</a> notes that if <span class="math-container">$L_1$</span> and <span class="math-container">$L_2$</span> are regular tree languages, than <span class="math-container">$L_1 \setminus L_2$</span> is as well. However, it doesn't define this quotient operation for trees, and doesn't give a reference for this specific fact.</p>

<p>I'm wondering if someone can point me to a formal definition of the quotient operaiton on tree languages, and a proof that they are indeed closed under this operation.</p>

CC BY-SA 4.0
2019-04-26T07:41:02.553Z
Are you sure that the symbol is not intended to denote set difference?
Jan Johannsen
CC BY-SA 4.0
2019-04-26T16:02:55.660Z
@JanJohannsen... derp. Yep, that's probably exactly what it is.
Joey Eremondi
<reference-request><fl.formal-languages><automata-theory><tree>
Regular Tree Languages are closed under quotient?
Joey Eremondi
# Regular Tree Languages are closed under quotient?

(Asked by: username_0 on 2019-04-25)

The [Wikipedia page for Regular Tree Grammars](https://en.wikipedia.org/wiki/Regular_tree_grammar) notes that if $L\_1$ and $L\_2$ are regular tree languages, than $L\_1 \setminus L\_2$ is as well. However, it doesn't define this quotient operation for trees, and doesn't give a reference for this specific fact.

I'm wondering if someone can point me to a formal definition of the quotient operaiton on tree languages, and a proof that they are indeed closed under this operation.

**Tags:** reference-request, fl.formal-languages, automata-theory, tree
> **Comments:**
> **username_1**: Are you sure that the symbol is not intended to denote set difference?  
> **username_0**: @JanJohannsen... derp. Yep, that's probably exactly what it is.  

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## 0 answers

