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

Helmut Seidl, Sebastian Maneth, Gregor Kemper

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 corandomized 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.
Original languageEnglish
Title of host publicationFoundations of Computer Science (FOCS), 2015 IEEE 56th Annual Symposium on
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages943 - 962
Number of pages20
Publication statusPublished - 20 Oct 2015


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