Decision problems of tree transducers with origin

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Abstract

A tree transducer with origin translates an input tree into a pair of output tree and origin info. The origin info maps each node in the output tree to the unique input node that created it. In this way, the implementation of the transducer becomes part of its semantics. We show that the landscape of decidable properties changes drastically when origin info is added. For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are undecidable without origin. The equivalence of deterministic topdown tree-to-string transducers is decidable with origin, while without origin it is a long standing open problem. With origin, we can decide if a deterministic macro tree transducer can be realized by a deterministic top-down tree transducer; without origin this is an open problem.

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Filiot, E., Maneth, S., Reynier, P. A., & Talbot, J. M. (2015). Decision problems of tree transducers with origin. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9135, pp. 209–221). Springer Verlag. https://doi.org/10.1007/978-3-662-47666-6_17

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