Timed Temporal Logics for Abstracting Transient States

In previous work, the timed logic TCTL was extended with an “almost everywhere” Until modality which abstracts negligible sets of positions (i.e. with a null duration) along a run of a timed automaton. We propose here an extension of this logic with more powerful modalities, in order to specify properties abstracting transient states, which are events that last for less than k time units. Our main result is that model-checking is still decidable and PSPACE-complete for this extension. On the other hand, a second semantics is defined, in which we consider the total duration where the property does not hold along a run. In this case, we prove that model-checking is undecidable.