Abstract
This paper presents a verification technique for dense-time MTL based on discretization. The technique reduces the validity problem of MTL formulas from dense to discrete time, through the notion of sampling invariance, introduced in previous work [13]. Since the reduction is from an undecidable problem to a decidable one, the technique is necessarily incomplete, so it fails to provide conclusive answers for some formulas. The paper discusses this shortcoming and hints at how it can be mitigated in practice. The verification technique has been implemented on top of the ℤot tool [19] for discrete-time bounded validity checking; the paper also reports on in-the-small experiments with the tool, which show some results that are promising in terms of performance.
Work partially supported by MIUR under the FIRB ArtDeco project.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abadi, M., Lamport, L.: An old-fashioned recipe for real-time. ACM TOPLAS 16(5), 1543–1571 (1994)
Alur, R., Henzinger, T.A.: Real-time logics: Complexity and expressiveness. Information and Computation 104(1), 35–77 (1993)
Biere, A., Heljanko, K., Junttila, T., Latvala, T., Schuppan, V.: Linear encodings of bounded LTL model checking. Logical Methods in Comp. Sci. 2(5:5), 1–64 (2006)
Chakravorty, G., Pandya, P.K.: Digiziting interval duration logic. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 167–179. Springer, Heidelberg (2003)
Ciapessoni, E., Coen-Porisini, A., Crivelli, E., Mandrioli, D., Mirandola, P., Morzenti, A.: From formal models to formally-based methods: an industrial experience. ACM TOSEM 8(1), 79–113 (1999)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)
de Alfaro, L., Manna, Z.: Verification in continuous time by discrete reasoning. In: AMAST 1995. LNCS, vol. 936, pp. 292–306 (1995)
D. D’Souza, R. Mohan M., and P. Prabhakar. Eliminating past operators in metric temporal logic. Technical Report IISc-CSA-TR-2006-11 (2006)
Fainekos, G.E., Pappas, G.J.: Robust Sampling for MITL Specifications. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 147–162. Springer, Heidelberg (2007)
Furia, C.A.: Scaling up the formal analysis of real-time systems. PhD thesis, DEI, Politecnico di Milano (May 2007)
Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M.: Modeling time in computing: A taxonomy and a comparative survey. Technical Report 2007.22, DEI, Politecnico di Milano (2007)
Furia, C.A., Pradella, M., Rossi, M.: Dense-time MTL verification through sampling. Technical Report 2007.37, DEI, Politecnico di Milano (April 2007)
Furia, C.A., Rossi, M.: Integrating Discrete- and Continuous-Time Metric Temporal Logics Through Sampling. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 215–229. Springer, Heidelberg (2006)
Furia, C.A., Rossi, M.: On the expressiveness of MTL variants over dense time. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 163–178. Springer, Heidelberg (2007)
Henzinger, T.A.: It’s about time: Real-time logics reviewed. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 439–454. Springer, Heidelberg (1998)
Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)
Hirshfeld, Y., Rabinovich, A.M.: Logics for real time: Decidability and complexity. Fundamenta Informaticae 62(1), 1–28 (2004)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)
Pradella, M.: Zot (March 2007), http://home.dei.polimi.it/pradella
Pradella, M., Morzenti, A., San Pietro, P.: The symmetry of the past and of the future. In: Proc. of ESEC/FSE 2007 (2007)
Sharma, B., Pandya, P.K., Chakraborty, S.: Bounded validity checking of interval duration logic. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 301–316. Springer, Heidelberg (2005)
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 and ProCoS 1994. LNCS, vol. 863, pp. 694–715. Springer, Heidelberg (1994)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Furia, C.A., Pradella, M., Rossi, M. (2008). Automated Verification of Dense-Time MTL Specifications Via Discrete-Time Approximation. In: Cuellar, J., Maibaum, T., Sere, K. (eds) FM 2008: Formal Methods. FM 2008. Lecture Notes in Computer Science, vol 5014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68237-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-68237-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68235-6
Online ISBN: 978-3-540-68237-0
eBook Packages: Computer ScienceComputer Science (R0)