A Diamond Structure in the Transducer Hierarchy
Formal Languages and Automata Theory
2025-12-17 v4 Logic
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.
Keywords
Cite
@article{arxiv.2111.05481,
title = {A Diamond Structure in the Transducer Hierarchy},
author = {Noah Kaufmann},
journal= {arXiv preprint arXiv:2111.05481},
year = {2025}
}