Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable
Abstract
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total transducers with unary output alphabet (over a given top-down regular domain language), and co-randomized polynomial time for linear transducers; these results are obtained using techniques from multi-linear algebra. For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals. This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence. Furthermore, we extend our result to deterministic top-down tree-to-string transducers which produce output not in a free monoid but in a free group.
Cite
@article{arxiv.1503.09163,
title = {Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable},
author = {Helmut Seidl and Sebastian Maneth and Gregor Kemper},
journal= {arXiv preprint arXiv:1503.09163},
year = {2017}
}