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# Learning Top-Down Tree Transducers with Regular Domain Inspection

*Proceedings of The 13th International Conference on Grammatical Inference*, PMLR 57:54-65, 2017.

#### Abstract

We study the problem of how to learn tree transformations on a given regular tree domain from a finite sample of input-output examples. We assume that the target tree transformation can be defined by a deterministic top-down tree transducer with regular domain inspection (DTOPIreg). An RPNI style learning algorithm that solves this problem in polynomial time and with polynomially many examples was presented at Pods’2010, but restricted to the case of path-closed regular domains. In this paper, we show that this restriction can be removed. For this, we present a new normal form for DTOPIreg by extending the Myhill-Nerode theorem for DTOP to regular domain inspections in a nontrivial manner. The RPNI style learning algorithm can also be lifted but becomes more involved too.