Closure properties of repetitive automata with translucent words

Determine the closure and non-closure properties of the language classes L(RNFAwtw) and L(RDFAwtw), where RNFAwtw and RDFAwtw denote repetitive nondeterministic and deterministic finite automata with translucent words, respectively, so as to identify which standard language operations preserve or fail to preserve these classes.

Background

The paper introduces repetitive variants of finite automata with translucent words and shows major expressiveness increases, including non–semi-linear languages and undecidable decision problems for RDFAwtws. Despite these advances, the authors note that systematic closure and non-closure properties for the repetitive models remain unsettled.

Earlier work established various closure properties for non-repetitive models (e.g., NFAwtw languages being semi-linear and possessing regular letter-equivalent sublanguages), but those results do not carry over in general to the repetitive setting. The paper provides some isolated non-closure examples (e.g., for RDFAwtw under union and alphabetic morphisms) and a complement-related simulation to RNFAwtw, motivating a comprehensive determination of closure behavior.