Abstract
Metric Interval Temporal Logic ( MITL
) is a well studied real-time, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITLrely on the automata theoretic approach, where logic formulas are translated into equivalent timed automata. Since timed automata are not closed under complementation, decision procedures for MITLfirst convert a formula into negated normal form before translating to a timed automaton. We show that, unfortunately, these 20-year-old procedures are incorrect, because they rely on an incorrect semantics of the \(\mathcal {R}\) operator. We present the right semantics of \(\mathcal {R}\) and give new, correct decision procedures for MITL. We show that both satisfiability and model checking for MITLare 
, as was previously claimed. We also identify a fragment of MITLthat we call MITL
WIthat is richer than \(\texttt {MITL}_{0,\!\infty }\), for which we show that both satisfiability and model checking are 
. Many of our results have been formally proved in PVS
Part of this work was carried out while the first author was at the University of Illinois, Urbana-Champaign.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Dill, D.L.: A Theory of Timed Automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., Feder, T., Henzinger, T.A.: The Benefits of Relaxing Punctuality. J. ACM 43(1), 116–146 (1996)
Bouyer, P., Markey, N., Reynier, P.-A.: Robust analysis of timed automata via channel machines. In: Amadio, R. (ed.) FoSSaCS 2008. LNCS, vol. 4962, pp. 157–171. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78499-9_12
Brihaye, T., Estiévenart, M., Geeraerts, G.: On MITL and alternating timed automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 47–61. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40229-6_4
Brihaye, T., Estiévenart, M., Geeraerts, G.: On MITL and alternating timed automata over infinite words. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 69–84. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_6
Hirshfeld, Y., Rabinovich, A.: Logics for Real Time: Decidability and Complexity. Fundam. Inf. 62(1), 1–28 (2004)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)
Maler, O., Nickovic, D., Pnueli, A.: From MITL to timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 274–289. Springer, Heidelberg (2006). https://doi.org/10.1007/11867340_20
Madhavan M.: Finite-state Automata on Infinite Inputs (1996)
Ouaknine, J., Worrell, J.: Some recent results in metric temporal logic. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 1–13. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85778-5_1
Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55602-8_217
Pnueli, A.: The Temporal Logic of Programs. In: SFCS, pp. 46–57. IEEE Computer Society (1977)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Roohi, N., Viswanathan, M. (2018). Revisiting MITL to Fix Decision Procedures. In: Dillig, I., Palsberg, J. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2018. Lecture Notes in Computer Science(), vol 10747. Springer, Cham. https://doi.org/10.1007/978-3-319-73721-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-73721-8_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73720-1
Online ISBN: 978-3-319-73721-8
eBook Packages: Computer ScienceComputer Science (R0)