Abstract
We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential blowup in the syntactic size of the monitors, and a triple-exponential blowup when the goal is a deterministic monitor. We show that these bounds are tight and that they also hold for translations between corresponding fragments of Hennessy-Milner logic with recursion over infinite traces.
Keywords
This research was partially supported by the projects “TheoFoMon: Theoretical Foundations for Monitorability” (grant number: 163406-051) and “Epistemic Logic for Distributed Runtime Monitoring” (grant number: 184940-051) of the Icelandic Research Fund, by the BMBF project “Aramis II” (project number: 01IS160253) and the EPSRC project “Solving parity games in theory and practice” (project number: EP/P020909/1).
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Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A.: Monitoring for silent actions. In: Lokam, S., Ramanujam, R. (eds.) FSTTCS. LIPIcs, vol. 93, pp. 7:1–7:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2017)
Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Kjartansson, S.Ö.: Determinizing monitors for HML with recursion. CoRR abs/1611.10212 (2016). http://arxiv.org/abs/1611.10212
Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Kjartansson, S.Ö.: On the complexity of determinizing monitors. In: Carayol, A., Nicaud, C. (eds.) CIAA 2017. LNCS, vol. 10329, pp. 1–13. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60134-2_1
Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Lehtinen, K.: Adventures in monitorability: from branching to linear time and back again. Proc. ACM Program. Lang. 3, 52:1–52:29 (2019). https://doi.org/10.1145/3290365. https://dl.acm.org/citation.cfm?id=3290365
Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Lehtinen, K.: The cost of monitoring alone. CoRR abs/1902.05152 (2019). http://arxiv.org/abs/1902.05152
Aceto, L., Cassar, I., Francalanza, A., Ingólfsdóttir, A.: On runtime enforcement via suppressions. In: Schewe, S., Zhang, L. (eds.) 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), vol. 118, pp. 34:1–34:17. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2018). https://doi.org/10.4230/LIPIcs.CONCUR.2018.34. http://drops.dagstuhl.de/opus/volltexte/2018/9572
Aceto, L., Ingólfsdóttir, A., Larsen, K.G., Srba, J.: Reactive Systems: Modelling, Specification and Verification. Cambridge Univ. Press, New York (2007). https://doi.org/10.1017/cbo9780511814105
Bartocci, E., Falcone, Y., Francalanza, A., Reger, G.: Introduction to runtime verification. In: Bartocci, E., Falcone, Y. (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 1–33. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75632-5_1
Bauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. ACM Trans. Softw. Eng. Methodol. 20(4), 1–64 (2011). https://doi.org/10.1145/2000799.2000800
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981). https://doi.org/10.1145/322234.322243
Falcone, Y., Fernandez, J.C., Mounier, L.: What can you verify and enforce at runtime? Int. J. Softw. Tools Technol. Transf. 14(3), 349–382 (2012). https://doi.org/10.1007/s10009-011-0196-8
Fellah, A., Jürgensen, H., Yu, S.: Constructions for alternating finite automata\(\ast \). Int. J. Comput. Math. 35(1–4), 117–132 (1990). https://doi.org/10.1080/00207169008803893
Francalanza, A., et al.: A foundation for runtime monitoring. In: RV, pp. 8–29 (2017). https://doi.org/10.1007/978-3-319-67531-2_2
Francalanza, A., Aceto, L., Ingolfsdottir, A.: Monitorability for the Hennessy–Milner logic with recursion. Form. Methods Syst. Des. 51(1), 87–116 (2017). https://doi.org/10.1007/s10703-017-0273-z
Kozen, D.C.: Results on the propositional \(\mu \)-calculus. Theor. Comput. Sci. 27, 333–354 (1983). https://doi.org/10.1016/0304-3975(82)90125-6
Larsen, K.G.: Proof systems for satisfiability in Hennessy-Milner logic with recursion. Theor. Comput. Sci. (TCS) 72(2), 265–288 (1990). https://doi.org/10.1016/0304-3975(90)90038-J. http://www.sciencedirect.com/science/article/pii/030439759090038J
Pnueli, A., Zaks, A.: PSL model checking and run-time verification via testers. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 573–586. Springer, Heidelberg (2006). https://doi.org/10.1007/11813040_38
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Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Lehtinen, K. (2019). The Cost of Monitoring Alone. In: Bartocci, E., Cleaveland, R., Grosu, R., Sokolsky, O. (eds) From Reactive Systems to Cyber-Physical Systems. Lecture Notes in Computer Science(), vol 11500. Springer, Cham. https://doi.org/10.1007/978-3-030-31514-6_15
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