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arXiv · 2606.30013

Preservation Theorems for Transducer Outputs

Valérie Berthé·Herman Goulet-Ouellet·Toghrul Karimov·Dominique Perrin·Mihir Vahanwala
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Abstract

Suppose we have a deterministic finite-state transducer $A$ and an infinite word $x$, and run $A$ on $x$ to obtain an infinite word $A(x)$. Which properties of $x$ are guaranteed to also hold for $A(x)$? In this paper, we study this preservation question for various well-known combinatorial properties, e.g., recurrence, being morphic, and having factor frequencies. The celebrated Krohn-Rhodes theorem provides the framework for proving our preservation results, and our techniques are based on the ergodic theory of symbolic dynamical systems, i.e., shift spaces.

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Valérie Berthé, Herman Goulet-Ouellet, Toghrul Karimov, Dominique Perrin, Mihir Vahanwala. 2026-06-29. Preservation Theorems for Transducer Outputs. https://arxiv.org/abs/2606.30013

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