Time-Bounded Verification

Joël Ouaknine, Alexander Rabinovich, James Worrell

Abstract: 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.