Acceptance of the deterministic linear language by RDFAwtw

Determine whether the deterministic linear language L_lin = { a^n b^n | n ≥ 1 } is accepted by any repetitive deterministic finite automaton with translucent words (RDFAwtw).

Background

The paper shows that L_lin is not accepted by any NFAwtw, but it constructs RDFAwtws accepting the even and odd-length sublanguages L_{2lin} = { a^{2n} b^{2n} | n ≥ 1 } and L_{2lin1} = { a^{2n+1} b^{2n+1} | n ≥ 0 }, and an RNFAwtw accepting L_lin via disjoint union.

Despite these constructions, it remains unresolved whether a single RDFAwtw (deterministic repetitive model) can accept the full language L_lin.