Abstract
Runtime verification and model checking are two important methods for assessing correctness of systems. In both techniques, detecting an error is witnessed by an execution that violates the system specification. However, a faulty execution on its own may not provide sufficiently precise insight to the causes of the reported violation. Additional, often manual effort is required to properly diagnose the system. In this paper we present a method for analyzing such causes. The specifications we consider are expressed in LTL (Linear Temporal Logic) and MTL (Metric Temporal Logic), and the execution models are taken as ultimately-periodic words, and finite variability continuous signals respectively. The diagnostics problem is defined for the propositional case as the search for a small implicant of a formula which is satisfied by a given valuation, or equivalently a subset of that valuation sufficient to render the formula true. We propose a suitable notion of implicants in the temporal case, that are semantically based on signal subsets, and guarantee the existence of prime implicants for arbitrary temporal properties. An inductive procedure for finding temporal implicants is obtained by the introduction of selection functions that appear in a process equivalent to Skolemization in first order logic. Through the model restrictions we impose for LTL and MTL we are able to generate concise implicants of a property, describing a small fragment of the input signal that causes violation of a formula.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beer, I., Ben-David, S., Chockler, H., Orni, A., Trefler, R.: Explaining counterexamples using causality. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 94–108. Springer, Heidelberg (2009)
Bienvenu, M.: Prime implicates and prime implicants: from propositional to modal logic. J. Artif. Intell. Res. 36(1), 71–128 (2009)
Bouyer, P., Markey, N., Ouaknine, J., Worrell, J.B.: On expressiveness and complexity in real-time model checking. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 124–135. Springer, Heidelberg (2008)
D’Souza, D., Tabareau, N.: On timed automata with input-determined guards. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 68–83. Springer, Heidelberg (2004)
Groce, A.: Error explanation with distance metrics. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 108–122. Springer, Heidelberg (2004)
Halpern, J.Y., Pearl, J.: Causes and explanations: a structural-model approach: Part 1: Causes. In: Uncertainty in Artificial Intelligence, pp. 194–202 (2001)
Hantry, F., Hacid, M.-S.: Handling conflicts in depth-first search for LTL tableau to debug compliance based languages. In: Formal Languages and Analysis of Contract-Oriented Software, pp. 39–53 (2011)
Jobstmann, B., Staber, S., Griesmayer, A., Bloem, R.: Finding and fixing faults. J. Comput. Syst. Sci. 78(2), 441–460 (2012)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)
Kupferman, O., Vardi, M.Y.: Model checking of safety properties. Formal Methods Syst. Des. 19(3), 291–314 (2001)
Maler, O., Nickovic, D.: Monitoring properties of analog and mixed-signal circuits. STTT 15(3), 247–268 (2013)
Markey, N., Raskin, J.-F.: Model checking restricted sets of timed paths. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 432–447. Springer, Heidelberg (2004)
Mukherjee, S., Dasgupta, P.: Computing minimal debugging windows in failure traces of AMS assertions. IEEE Trans. CAD Integr. Circ. Syst. 31(11), 1776–1781 (2012)
Pill, I., Semprini, S., Cavada, R., Roveri, M., Bloem, R., Cimatti, A.: Formal analysis of hardware requirements. In: Design Automation Conference, pp. 821–826 (2006)
Pnueli, A.: The temporal logic of programs. In: Foundations of Computer Science, pp. 46–57. IEEE (1977)
Schuppan, V.: Towards a notion of unsatisfiable and unrealizable cores for LTL. Sci. Comput. Program. 77(7–8), 908–939 (2012)
Schuppan, V., Biere, A.: Shortest counterexamples for symbolic model checking of LTL with past. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 493–509. Springer, Heidelberg (2005)
Acknowledgements
This work was supported by ANR project CADMIDIA, and the MISTRAL project A-1341-RT-GP coordinated by the European Defence Agency (EDA) and funded by 8 contributing Members (France, Germany, Italy, Poland, Austria, Sweden, Netherland and Luxenbourg) in the framework of the Joint Investment Programme on Second Innovative Concepts and Emerging Technologies (JIP-ICET 2) and the IKT der Zukunft of Austrian FFG project HARMONIA (nr. 845631).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ferrère, T., Maler, O., Ničković, D. (2015). Trace Diagnostics Using Temporal Implicants. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-24953-7_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24952-0
Online ISBN: 978-3-319-24953-7
eBook Packages: Computer ScienceComputer Science (R0)