We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when restricting to functions from words to words. Here we prove that decidability can be equally recovered by adopting a slightly different, but natural semantics, called origin semantics and introduced by Bojanczyk in 2014. Specifically, we prove that the equivalence and containment problems for two-way word transducers in the origin semantics are PSPACE-complete. We also consider a variant of the containment problem where two-way transducers are compared under the origin semantics, but in a more relaxed way, by allowing distortions of the origins. The possible distortions are described by means of a resynchronization relation. We propose a logical formalism for describing a broad class of resynchronizations, while preserving the decidability of the variant of the containment problem.
from cs updates on arXiv.org https://ift.tt/2ObUecX
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