On Metric Temporal Logic and Faulty Turing Machines

Metric Temporal Logic (MTL) is a real-time extension of Linear Temporal Logic that was proposed fifteen years ago and has since been extensively studied. Since the early 1990s, it has been widely believed that some very small fragments of MTL are undecidable (i.e., have undecidable satisfiability and model-checking problems). We recently showed that, on the contrary, some substantial and important fragments of MTL are decidable [19, 20]. However, until now the question of the decidability of full MTL over infinite timed words remained open. In this paper, we settle the question negatively. The proof of undecidability relies on a surprisingly strong connection between MTL and a particular class of faulty Turing machines, namely ‘insertion channel machines with emptiness-testing’.