# #StackBounty: #formal-languages #formal-grammars #trees #tree-grammars Unranked trees grammars?

### Bounty: 50

Ranked alphabet is very often used in Ranked Trees definition, like here for instance. In that example for given set \$Sigma={a,b,c}\$ ranks assigned by arity function \$ar : Sigmarightarrowmathcal{N}\$ as:

\$ar(a)=2, ar(b)=2, ar(c)=1\$.

And Ranked Tree over \$Sigma\$ is defined as:

\$T_{Sigma_r}\$, the set of ranked trees, is the smallest set of terms \$f(t_1,dots,t_k)\$ such that: \$finSigma_r\$, \$k = ar(f)\$, and \$t_iin T_{Sigma_r}\$ for all \$1leq ileq k\$.

The tree in this example looks like:

``````       b
/
a     b
/    /
b   c c   c
/
c   c
``````

But what about trees like that?

``````       b
/
a     b
/    /
b   c c   c
|   |
c   a
``````

This is also valid tree, but it is obviously is unranked.

My question: do any research regarding unranked alphabet trees exist?

What I’ve found so far is related only to logic for unranked trees.

Get this bounty!!!

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