Time-bounded verification

Joël Ouaknine*, Alexander Rabinovich, James Worrell

*Corresponding author for this work

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


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


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