Abstract
We consider the problem of modelling and verifying the behaviour of systems characterised by a close interaction of a program with the environment. We propose to model the program-environment interplay in terms of the probabilistic modifications they induce on a set of application-relevant data, called data space. The behaviour of a system is thus identified with the probabilistic evolution of the initial data space. Then, we introduce a metric, called evolution metric, measuring the differences in the evolution sequences of systems and that can be used for system verification as it allows for expressing how well the program is fulfilling its tasks. We use the metric to express the properties of adaptability and reliability of a program, which allow us to identify potential critical issues of it w.r.t. changes in the initial environmental conditions. We also propose an algorithm, based on statistical inference, for the evaluation of the evolution metric.
This work has been partially supported by the IRF project “OPEL” (grant No. 196050-051) and by the PRIN project “IT-MaTTerS” (grant No. 2017FTXR7S).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Abate, A., D’Innocenzo, A., Benedetto, M.D.D.: Approximate abstractions of stochastic hybrid systems. IEEE Trans. Automat. Contr. 56(11), 2688–2694 (2011)
Abate, A., Katoen, J., Lygeros, J., Prandini, M.: Approximate model checking of stochastic hybrid systems. Eur. J. Control. 16(6), 624–641 (2010)
Abate, A., Prandini, M.: Approximate abstractions of stochastic systems: a randomized method. In: Proceedings of CDC-ECC 2011, pp. 4861–4866 (2011)
Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. In: Proceedings of ICML 2017, pp. 214–223 (2017)
Bernardo, M., Nicola, R.D., Loreti, M.: A uniform framework for modeling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences. Inf. Comput. 225, 29–82 (2013)
Bloom, H.A.P., Lygeros, J. (eds.): Stochastic Hybrid Systems: Theory and Safety Critical Applications. Lecture Notes in Control and Information Sciences, vol. 337. Springer, Heidelberg (2006). https://doi.org/10.1007/11587392
Breugel, F.: A behavioural pseudometric for metric labelled transition systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 141–155. Springer, Heidelberg (2005). https://doi.org/10.1007/11539452_14
Cassandras, C.G., Lygeros, J. (eds.): Stochastic Hybrid Systems. Control Engineering, vol. 24, 1st edn. CRC Press, Boca Raton (2007)
Castiglioni, V., Chatzikokolakis, K., Palamidessi, C.: A logical characterization of differential privacy via behavioral metrics. In: Bae, K., Ölveczky, P.C. (eds.) FACS 2018. LNCS, vol. 11222, pp. 75–96. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02146-7_4
Castiglioni, V., Chatzikokolakis, K., Palamidessi, C.: A logical characterization of differential privacy. Sci. Comput. Program. 188, 102388 (2020)
Castiglioni, V., Loreti, M., Tini, S.: Measuring adaptability and reliability of large scale systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2020. LNCS, vol. 12477, pp. 380–396. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61470-6_23
Castiglioni, V., Loreti, M., Tini, S.: The metric linear-time branching-time spectrum on nondeterministic probabilistic processes. Theor. Comput. Sci. 813, 20–69 (2020)
Castro, P.F., D’Argenio, P.R., Demasi, R., Putruele, L.: Measuring masking fault-tolerance. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019, Part II. LNCS, vol. 11428, pp. 375–392. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17465-1_21
Cerný, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. Theor. Comput. Sci. 413(1), 21–35 (2012)
Chatzikokolakis, K., Gebler, D., Palamidessi, C., Xu, L.: Generalized bisimulation metrics. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 32–46. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44584-6_4
Ciocchetta, F., Hillston, J.: Bio-PEPA: an extension of the process algebra PEPA for biochemical networks. Electron. Notes Theor. Comput. Sci. 194(3), 103–117 (2008)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. Theor. Comput. Sci. 318(3), 323–354 (2004)
Deshmukh, J.V., Majumdar, R., Prabhu, V.S.: Quantifying conformance using the skorokhod metric. Formal Methods Syst. Design 50(2–3), 168–206 (2017)
Faugeras, O.P., Rüschendorf, L.: Risk excess measures induced by hemi-metrics. Probab. Uncertain. Quant. Risk 3(1), 1–35 (2018). https://doi.org/10.1186/s41546-018-0032-0
Gebler, D., Larsen, K.G., Tini, S.: Compositional bisimulation metric reasoning with probabilistic process calculi. Log. Methods Comput. Sci. 12(4) (2016)
Ghosh, S., Bansal, S., Sangiovanni-Vincentelli, A.L., Seshia, S.A., Tomlin, C.: A new simulation metric to determine safe environments and controllers for systems with unknown dynamics. In: Proceedings of HSCC 2019, pp. 185–196 (2019)
Giacalone, A., Jou, C.C., Smolka, S.A.: Algebraic reasoning for probabilistic concurrent systems. In: Proceedings of IFIP Work, Conference on Programming, Concepts and Methods, pp. 443–458 (1990)
Girard, A., Gößler, G., Mouelhi, S.: Safety controller synthesis for incrementally stable switched systems using multiscale symbolic models. IEEE Trans. Automat. Contr. 61(6), 1537–1549 (2016)
van Glabbeek, R.J., Smolka, S.A., Steffen, B.: Reactive, generative and stratified models of probabilistic processes. Inf. Comput. 121(1), 59–80 (1995)
Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.C.: Improved training of Wasserstein GANs. In: Proceedings of Advances in Neural Information Processing Systems, pp. 5767–5777 (2017)
Heredia, G., et al.: Control of a multirotor outdoor aerial manipulator. In: Proceedings of IROS 2014, pp. 3417–3422. IEEE (2014)
Hillston, J., Hermanns, H., Herzog, U., Mertsiotakis, V., Rettelbach, M.: Stochastic process algebras: integrating qualitative and quantitative modelling. In: Proceedings of International Conference on Formal Description Techniques 1994. IFIP, vol. 6, pp. 449–451 (1994)
Hu, J., Lygeros, J., Sastry, S.: Towards a theory of stochastic hybrid systems. In: Lynch, N., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 160–173. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-46430-1_16
Kwiatkowska, M., Norman, G.: Probabilistic metric semantics for a simple language with recursion. In: Penczek, W., Szałas, A. (eds.) MFCS 1996. LNCS, vol. 1113, pp. 419–430. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61550-4_167
Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12
Malhame, R., Yee Chong, C.: Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system. IEEE Trans. Automat. Contr. 30(9), 854–660 (1985)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Statistics. Wiley, USA (2005)
Rachev, S.T., Klebanov, L.B., Stoyanov, S.V., Fabozzi, F.J.: The Methods of Distances in the Theory of Probability and Statistics. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4614-4869-3
Segala, R.: Modeling and verification of randomized distributed real-time systems. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, USA (1995)
Skorokhod, A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290 (1956)
Sriperumbudur, B.K., Fukumizu, K., Gretton, A., Schölkopf, B., Lanckriet, G.R.G.: On the empirical estimation of integral probability metrics. Electron. J. Stat. 6, 1550–1599 (2021)
Thorsley, D., Klavins, E.: Approximating stochastic biochemical processes with Wasserstein pseudometrics. IET Syst. Biol. 4(3), 193–211 (2010)
Tolstikhin, I.O., Bousquet, O., Gelly, S., Schölkopf, B.: Wasserstein auto-encoders. In: Proceedings of ICLR 2018 (2018)
Vaserstein, L.N.: Markovian processes on countable space product describing large systems of automata. Probl. Peredachi Inf. 5(3), 64–72 (1969)
Villani, C.: Optimal Transport: Old and New, vol. 338. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71050-9
Virágh, C., Nagy, M., Gershenson, C., Vásárhelyi, G.: Self-organized UAV traffic in realistic environments. In: Proceedings of IROS 2016, pp. 1645–1652. IEEE (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 IFIP International Federation for Information Processing
About this paper
Cite this paper
Castiglioni, V., Loreti, M., Tini, S. (2021). How Adaptive and Reliable is Your Program?. In: Peters, K., Willemse, T.A.C. (eds) Formal Techniques for Distributed Objects, Components, and Systems. FORTE 2021. Lecture Notes in Computer Science(), vol 12719. Springer, Cham. https://doi.org/10.1007/978-3-030-78089-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-78089-0_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78088-3
Online ISBN: 978-3-030-78089-0
eBook Packages: Computer ScienceComputer Science (R0)