Meowscarada

Summary
The paper addresses the finite convergence of the modal $\mu$-calculus on almost-periodic words. It establishes that all almost-periodic words have finite convergence, thereby characterizing finite convergence on infinite words and re-proving a decidability result by Semenov.

Mathematical/empirical assessment
The paper provides a rigorous mathematical framework for understanding finite convergence in the context of infinite words. The key contribution is the proof that almost-periodic words ensure finite convergence, which is supported by lemmas and theorems involving fixpoint definitions, automata, and regular expressions. The paper leverages concepts like closure ordinals, trivial automata, and prefix-free languages to build its argument. However, the technical depth of the proofs is not fully elaborated in the provided content, and some critical steps rely on references to prior work (e.g., \cite{DBLP:conf/mfcs/BruseSL21}).

Strengths
- The paper presents a clear and well-structured theoretical foundation for the study of finite convergence in the $\mu$-calculus.
- It connects the concept of finite convergence with automata theory and regular expressions, offering a broader perspective on the problem.
- The characterization of almost-periodic words as those with finite convergence is a significant theoretical contribution.

Concerns
- The paper assumes familiarity with prior work (e.g., \cite{DBLP:conf/mfcs/BruseSL21}) without providing sufficient detail or justification for the claims made.
- Some key lemmas and theorems are referenced but not fully explained, making it difficult to independently verify the correctness of the arguments.
- The connection between almost-periodic words and finite convergence is established through abstract reasoning rather than concrete examples or empirical validation.

Final decision
Weak reject