Twentieth Annual IEEE Symposium on

Logic in Computer Science (LICS 2005)

Paper: On the Decidability of Metric Temporal Logic (at LICS 2005)

Authors: Joël Ouaknine James Worrell


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. The question of the decidability of MTL over infinite words remains open.


    author = 	 {Joël Ouaknine and James Worrell},
    title = 	 {On the Decidability of Metric Temporal Logic},
    booktitle =  {Proceedings of the Twentieth Annual IEEE Symp. on Logic in Computer Science, {LICS} 2005},
    year =	 2005,
    editor =	 {Prakash Panangaden},
    month =	 {June}, 
    pages =      {188--197},
    location =   {Chicago, USA}, 
    publisher =	 {IEEE Computer Society Press}