---
title: On the decidability and complexity of Metric Temporal Logic over finite words
url: https://www.emergentmind.com/papers/0702120
type: paper
arxiv_id: '0702120'
arxiv_url: https://arxiv.org/abs/0702120
published: '2007-02-21'
categories:
- cs.LO
- cs.CC
---

# On the decidability and complexity of Metric Temporal Logic over finite words

## Abstract

Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature.