Decidability of boundedness for DFAwtw (non-repetitive)

Determine whether the boundedness problem is decidable for deterministic finite automata with translucent words (DFAwtws).

Background

The paper proves that boundedness is undecidable for RDFAwtws by reduction from PCP. In contrast, for non-repetitive DFAwtws, the authors explicitly note that the decidability status of boundedness remains unresolved.

Boundedness asks whether a language is contained in a finite concatenation of starred words, and its decidability varies widely across automata models; solving this for DFAwtws would complete the status alongside the repetitive cases established in the paper.