TY - GEN
T1 - Time-bounded verification
AU - Ouaknine, Joël
AU - Rabinovich, Alexander
AU - Worrell, James
N1 - Funding Information:
This work was partially supported by the ESF Research Networking Programme Games and the UK’s EPSRC .
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70349871428&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-04081-8_33
DO - 10.1007/978-3-642-04081-8_33
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AN - SCOPUS:70349871428
SN - 3642040802
SN - 9783642040801
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 496
EP - 510
BT - CONCUR 2009 - Concurrency Theory - 20th International Conference, CONCUR 2009, Proceedings
T2 - 20th International Conference on Concurrency Theory, CONCUR 2009
Y2 - 1 September 2009 through 4 September 2009
ER -