In *20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)*, pages 188–197, 2005. ISBN: 0-7695-2266-1

Paper doi abstract bibtex

Paper doi abstract bibtex

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.

@inproceedings{ouaknine_decidability_2005, title = {On the decidability of metric temporal logic}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1509223%5Cnhttp://ieeexplore.ieee.org/document/1509223/}, doi = {10.1109/LICS.2005.33}, 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. The question of the decidability of MTL over infinite words remains open.}, booktitle = {20th {Annual} {IEEE} {Symposium} on {Logic} in {Computer} {Science} ({LICS}' 05)}, author = {Ouaknine, J. and Worrell, J.}, year = {2005}, note = {ISBN: 0-7695-2266-1}, keywords = {Abstracts, Alur-Dill timed automaton, Automata, Constraint theory, Laboratories, Logic, Mathematics, Real time systems, Safety, Timing, Turing machines, decidability, finite automata, metric temporal logic, model-checking problem, satisfiability problem, temporal logic}, pages = {188--197} }

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