On Equivalences for a Class of Timed Regular Expressions

AbstractTimed regular expressions are an extension of regular expressions that capture a notion of time. Roughly speaking, timed regular expressions can be used to represent timed sequences of events, with new operators to control the duration of those sequences. These timed regular expressions correspond to a form of timed automaton equipped with clocks, of the kind introduced by Alur and Dill. We develop a coalgebraic treatment of such timed regular expressions, along the lines of the coalgebraic treatment of regular expressions based on deterministic automata. This yields a coinductive proof principle, that can be used to establish equivalence of a class of timed regular expressions