Safety Metric Temporal Logic Is Fully Decidable

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we consider a fragment of MTL, called Safety MTL, capable of expressing properties such as invariance and time-bounded response. Our main result is that the satisfiability problem for Safety MTL is decidable. This is the first positive decidability result for MTL over timed ω-words that does not involve restricting the precision of the timing constraints, or the granularity of the semantics; the proof heavily uses the techniques of infinite-state verification. Combining this result with some of our previous work, we conclude that Safety MTL is fully decidable in that its satisfiability, model checking, and refinement problems are all decidable.