On the Balancedness of Tree-to-word Transducers

Raphaela Löbel; Michael Luttenberger; Helmut Seidl

On the Balancedness of Tree-to-word Transducers

Formal Languages and Automata Theory 2020-03-16 v2

Authors: Raphaela Löbel , Michael Luttenberger , Helmut Seidl

Abstract

A language over an alphabet $B = A \cup \overline{A}$ of opening ( $A$ ) and closing ( $\overline{A}$ ) brackets, is balanced if it is a subset of the Dyck language $D_B$ over $B$ , and it is well-formed if all words are prefixes of words in $D_B$ . We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time. With this at a hand we decide for the class 2-TWs of non-linear tree transducers with output alphabet $B^*$ whether or not the output language is balanced.

Keywords

tree-to-word transducers balanced language well-formed language dyck language context-free language 2-tw polynomial time

Cite

@article{arxiv.1911.13054,
  title  = {On the Balancedness of Tree-to-word Transducers},
  author = {Raphaela Löbel and Michael Luttenberger and Helmut Seidl},
  journal= {arXiv preprint arXiv:1911.13054},
  year   = {2020}
}

Comments

Major changes in Section 3 Balancedness of 2-TWs: instead of proving equivalence of LTWs over the involutive monoid we use the result that equivalence of LTWs over the free group is decidable in polynomial time (arXiv:2001.03480). A short version will be published in the conference proceedings of DLT 2020

On the Balancedness of Tree-to-word Transducers

Abstract

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