Expressive equivalence between extended timed regular expressions and timed automata

Determine which subclasses of timed automata are expressively equivalent to extended timed regular expressions that exclude the renaming operation and conjunction; specifically, characterize the class of timed automata whose timed languages can be denoted by timed regular expressions using only concatenation, union, Kleene star, time restriction, and the absorbing operators (concatenation and iteration), but without renaming and intersection, in order to clarify the boundary of applicability of TRE-based synthesis.

Background

Asarin, Caspi, and Maler established that generalized extended timed regular expressions (GEE), which include operations such as union, concatenation, Kleene star, time restriction, absorbing operators, intersection, and renaming, have the same expressive power as timed automata. However, the present work restricts attention to (extended) timed regular expressions without the renaming function and conjunction, motivated by the difficulty of inferring renaming from observed behaviors during synthesis.

Because the synthesis framework developed here operates within the (extended) TRE fragment lacking renaming and intersection, it may not capture all real-time scheduling models representable by general timed automata. This motivates a precise characterization of which timed automata remain expressively equivalent to the considered (extended) TRE fragment.