Accepting Zeno words: a way toward timed refinements

Abstract.

Timed models were introduced to describe the behaviors of real-time systems and they were usually required to produce only executions with divergent sequences of times. However, when some physical phenomena are represented by convergent executions, Zeno words appear in a natural way. Moreover, time can progress if such an infinite execution can be followed by other ones.

Therefore, in a first part, we extend the definition of timed automata, allowing to generate sequences of infinite convergent executions, while keeping good properties for the verification of systems: emptiness is still decidable.

In a second part, we define a new notion of refinement for timed systems, in which actions are replaced by recognizable Zeno (timed) languages. We study the properties of these timed refinements and we prove that the class of transfinite timed languages is the closure of the usual one (languages accepted by Muller or Büchi timed automata) under refinement.