2103.01012
Unambiguously coded systems
Marie-Pierre Béal, Dominique Perrin, Antonio Restivo
correcthigh confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that every coded system admits a countable strongly connected automaton that is deterministic, co-deterministic, and strongly unambiguous (Theorem 7), with a complete construction and proof. The candidate’s fiber-product construction establishes bideterminism and language equality but leaves an essential, unresolved gap: strong connectivity (and its interaction with strong unambiguity) is not derived for arbitrary coded systems. Hence the model does not solve the posed problem, while the paper does.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript presents a complete and well-structured proof that any coded system admits a countable strongly connected presentation that is both deterministic and co-deterministic and, crucially, strongly unambiguous. The argument is constructive and engages directly with the subtleties of injectivity on bi-infinite labels. While largely clear, a few steps could be made more accessible to a broad symbolic dynamics audience, especially the combinatorial core of the strong unambiguity proof and the preservation of bideterminism during the modification.