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

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2018 Journal of the ACM  
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
more » ... ce 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.
doi:10.1145/3182653 fatcat:ayyyao4j4ncfflbq6lboybjbru