Time-bounded verification

Joël Ouaknine*, Alexander Rabinovich, James Worrell

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

30 Scopus citations


We study the decidability and complexity of verification problems for timed automata over time intervals of fixed, bounded length. One of our main results is that time-bounded language inclusion for timed automata is 2EXPSPACE-Complete. We also investigate the satisfiability and model-checking problems for Metric Temporal Logic (MTL), as well as monadic first- and second-order logics over the reals with order and the +∈1 function (FO(∈<∈,∈+∈1) and MSO(∈<∈,∈+∈1) respectively). We show that, over bounded time intervals, MTL satisfiability and model checking are EXPSPACE-Complete, whereas these problems are decidable but non-elementary for the predicate logics. Nevertheless, we show that MTL and FO(∈<∈,∈+∈1) are equally expressive over bounded intervals, which can be viewed as an extension of Kamp's well-known theorem to metric logics. It is worth recalling that, over unbounded time intervals, the satisfiability and model-checking problems listed above are all well-known to be undecidable.

Original languageEnglish
Title of host publicationCONCUR 2009 - Concurrency Theory - 20th International Conference, CONCUR 2009, Proceedings
Number of pages15
StatePublished - 2009
Event20th International Conference on Concurrency Theory, CONCUR 2009 - Bologna, Italy
Duration: 1 Sep 20094 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5710 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Conference on Concurrency Theory, CONCUR 2009


FundersFunder number
ESF Research Networking Programme Games
Engineering and Physical Sciences Research Council


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