Time-bounded verification

We study the decidability and complexity of verification problems for timed automata over time intervals of fixed, bounded length. One of our main results is that time-bounded language inclusion for timed automata is 2EXPSPACE-Complete. We also investigate the satisfiability and model-checking problems for Metric Temporal Logic (MTL), as well as monadic first- and second-order logics over the reals with order and the +∈1 function (FO(∈<∈,∈+∈1) and MSO(∈<∈,∈+∈1) respectively). We show that, over bounded time intervals, MTL satisfiability and model checking are EXPSPACE-Complete, whereas these problems are decidable but non-elementary for the predicate logics. Nevertheless, we show that MTL and FO(∈<∈,∈+∈1) are equally expressive over bounded intervals, which can be viewed as an extension of Kamp's well-known theorem to metric logics. It is worth recalling that, over unbounded time intervals, the satisfiability and model-checking problems listed above are all well-known to be undecidable.