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arXiv · 2111.05481

A Diamond Structure in the Transducer Hierarchy

Noah Kaufmann
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Abstract

We answer an open question in the theory of transducer degrees on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which can be realized by a finite state transducer, which form an order based on which words can be transformed into other words. We provide a construction which proves the existence of a diamond structure, while also introducing a new function on streams which may be useful for proving more results about the transducer hierarchy.

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Noah Kaufmann. 2021-11-10. A Diamond Structure in the Transducer Hierarchy. https://doi.org/10.46298/dmtcs.8704

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