Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

Helmut Seidl; Sebastian Maneth; Gregor Kemper

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arXiv · 1503.09163

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

Helmut Seidl·Sebastian Maneth·Gregor Kemper

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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.

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BibTeX RIS

Helmut Seidl, Sebastian Maneth, Gregor Kemper. 2017-01-27. Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable. https://arxiv.org/abs/1503.09163

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