MTL with Bounded Variability: Decidability and Complexity
This paper investigates the properties of Metric Temporal Logic (MTL) over models in which time is dense but phenomena are constrained to have bounded variability. Contrary to the case of generic dense-time behaviors, MTL is proved to be fully decidable over models with bounded variability, if the variability bound is given. In these decidable cases, MTL complexity is shown to match that of simpler decidable logics such as MITL. On the contrary, MTL is undecidable if all behaviors with variability bounded by some generic constant are considered, but with an undecidability degree that is lower than in the case of generic behaviors.
Unable to display preview. Download preview PDF.
- 4.Bouyer, P., Markey, N., Ouaknine, J., Worrell, J.: The cost of punctuality. In: Proceedings of LICS 2007 (2007)Google Scholar
- 5.D’Souza, D., Prabhakar, P.: On the expressiveness of MTL in the pointwise and continuous semantics. Formal Methods Letters 9(1), 1–4 (2007)Google Scholar
- 6.M. Fränzle. Decidability of duration calculi on restricted model classes. Technical Report Kiel MF 21/1, Christian-Albrechts Universität Kiel (1996)Google Scholar
- 9.Furia, C.A., Rossi, M.: MTL with bounded variability: Decidability and complexity. Technical report, DEI, Politecnico di Milano (May 2008)Google Scholar
- 10.Gabbay, D.M., Hodkinson, I., Reynolds, M.: Temporal Logic, vol. 1. Oxford University Press, Oxford (1994)Google Scholar
- 14.Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Logical Methods in Computer Science 3(1) (2007)Google Scholar
- 16.Rabinovich, A.M.: Complexity of metric temporal logic with counting. In: Proceedings of FORMATS 2008. LNCS. Springer, Heidelberg (2008)Google Scholar
- 17.Wilke, T.: Specifying timed state sequences in powerful decidable logics and timed automata. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994. LNCS, vol. 863, pp. 694–715. Springer, Heidelberg (1994)Google Scholar