Abstract
Quantitative verification tools compute probabilities, expected rewards, or steady-state values for formal models of stochastic and timed systems. Exact results often cannot be obtained efficiently, so most tools use floating-point arithmetic in iterative algorithms that approximate the quantity of interest. Correctness is thus defined by the desired precision and determines performance. In this paper, we report on the experimental evaluation of these trade-offs performed in QComp 2020: the second friendly competition of tools for the analysis of quantitative formal models. We survey the precision guarantees—ranging from exact rational results to statistical confidence statements—offered by the nine participating tools. They gave rise to a performance evaluation using five tracks with varying correctness criteria, of which we present the results.
The authors are listed alphabetically. This work was supported by DFG grant 389792660 as part of TRR 248 (CPEC), DFG grant 383882557 (SUV), ERC Advanced Grant 787914 (FRAPPANT), ERC Advanced Grant 834115 (FUN2MODEL), ERC Advanced Grant 695614 (POWVER), the Guangdong Science and Technology Department (grant no. 2018B010107004), the National Natural Science Foundation of China (grant nos. 61761136011, 61532019, 61836005), National Science Foundation grant CCF-1856733, NWO project 15474 (SEQUOIA), and NWO VENI grant no. 639.021.754.
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Data Availability.
The tools used and data generated in the performance evaluation are archived at qcomp.org and DOI 10.5281/zenodo.3965313 [57].
Notes
- 1.
Storm, on the other hand, is not compared with Storm-static, thus its “wins n” numbers, marked *, are not part of the same sum as those of the other tools.
References
Abate, A., et al.: ARCH-COMP19 category report: stochastic modelling. In: ARCH. EPiC Series in Computing, vol. 61, pp. 62–102. EasyChair (2019). https://doi.org/10.29007/f2vb
Agha, G., Palmskog, K.: A survey of statistical model checking. ACM Trans. Model. Comput. Simul. 28(1), 6:1–6:39 (2018). https://doi.org/10.1145/3158668
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8
Amparore, E.G., Balbo, G., Beccuti, M., Donatelli, S., Franceschinis, G.: 30 years of GreatSPN. In: Fiondella, L., Puliafito, A. (eds.) Principles of Performance and Reliability Modeling and Evaluation, pp. 227–254. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30599-8_9
Arnold, F., Belinfante, A., van der Berg, F., Guck, D., Stoelinga, M.: DFTCalc: a tool for efficient fault tree analysis. In: SAFECOMP. LNCS, vol. 8153, pp. 293–301. Springer (2013). https://doi.org/10.1007/978-3-642-40793-2_27
Ashok, P., Butkova, Y., Hermanns, H., Kretínský, J.: Continuous-time Markov decisions based on partial exploration. In: ATVA. LNCS, vol. 11138, pp. 317–334. Springer (2018). https://doi.org/10.1007/978-3-030-01090-4_19
Ashok, P., Chatterjee, K., Daca, P., Kretínský, J., Meggendorfer, T.: Value iteration for long-run average reward in Markov decision processes. In: CAV. LNCS, vol. 10426, pp. 201–221. Springer (2017). https://doi.org/10.1007/978-3-319-63387-9_10
Ashok, P., Kretínský, J., Weininger, M.: PAC statistical model checking for Markov decision processes and stochastic games. In: CAV. LNCS, vol. 11561, pp. 497–519. Springer (2019). https://doi.org/10.1007/978-3-030-25540-4_29
Baier, C., de Alfaro, L., Forejt, V., Kwiatkowska, M.: Model checking probabilistic systems. In: Handbook of Model Checking, pp. 963–999. Springer (2018). https://doi.org/10.1007/978-3-319-10575-8_28
Baier, C., Katoen, J.P., Hermanns, H.: Approximate symbolic model checking of continuous-time Markov chains. In: CONCUR. LNCS, vol. 1664, pp. 146–161. Springer (1999). https://doi.org/10.1007/3-540-48320-9_12
Baier, C., Klein, J., Leuschner, L., Parker, D., Wunderlich, S.: Ensuring the reliability of your model checker: interval iteration for MDPs. In: CAV. LNCS, vol. 10426, pp. 160–180. Springer (2017). https://doi.org/10.1007/978-3-319-63387-9_8
Bauer, M.S., Mathur, U., Chadha, R., Sistla, A.P., Viswanathan, M.: Exact quantitative probabilistic model checking through rational search. In: FMCAD, pp. 92–99. IEEE (2017). https://doi.org/10.23919/FMCAD.2017.8102246
Behrmann, G., et al.: UPPAAL 4.0. In: QEST, pp. 125–126. IEEE Computer Society (2006). https://doi.org/10.1109/QEST.2006.59
Bonet, B., Geffner, H.: Labeled RTDP: improving the convergence of real-time dynamic programming. In: ICAPS, pp. 12–21. AAAI Press (2003)
Brázdil, T., Chatterjee, K., Chmelik, M., Forejt, V., Kretínský, J., Kwiatkowska, M.Z., Parker, D., Ujma, M.: Verification of Markov decision processes using learning algorithms. In: ATVA. LNCS, vol. 8837, pp. 98–114. Springer (2014). https://doi.org/10.1007/978-3-319-11936-6_8
Budde, C.E., D’Argenio, P.R., Hartmanns, A.: Better automated importance splitting for transient rare events. In: SETTA. LNCS, vol. 10606, pp. 42–58. Springer (2017). https://doi.org/10.1007/978-3-319-69483-2_3
Budde, C.E., D’Argenio, P.R., Hartmanns, A.: Automated compositional importance splitting. Sci. Comput. Program. 174, 90–108 (2019). DOI: 10.1016/j.scico.2019.01.006
Budde, C.E., D’Argenio, P.R., Hartmanns, A., Sedwards, S.: An efficient statistical model checker for nondeterminism and rare events. STTT (2020, to appear)
Budde, C.E., Dehnert, C., Hahn, E.M., Hartmanns, A., Junges, S., Turrini, A.: JANI: Quantitative model and tool interaction. TACAS. LNCS 10206, 151–168 (2017). https://doi.org/10.1007/978-3-662-54580-5_9
Butkova, Y., Fox, G.: Optimal time-bounded reachability analysis for concurrent systems. In: TACAS. LNCS, vol. 11428, pp. 191–208. Springer (2019). https://doi.org/10.1007/978-3-030-17465-1_11
Butkova, Y., Hartmanns, A., Hermanns, H.: A Modest approach to modelling and checking Markov automata. In: QEST. LNCS, vol. 11785, pp. 52–69. Springer (2019). https://doi.org/10.1007/978-3-030-30281-8_4
Butkova, Y., Hatefi, H., Hermanns, H., Krcál, J.: Optimal continuous time Markov decisions. In: ATVA. LNCS, vol. 9364, pp. 166–182. Springer (2015). https://doi.org/10.1007/978-3-319-24953-7_12
Butkova, Y., Wimmer, R., Hermanns, H.: Long-run rewards for Markov automata. TACAS. LNCS 10206, 188–203 (2017). https://doi.org/10.1007/978-3-662-54580-5_11
Ceska, M., Hensel, C., Junges, S., Katoen, J.P.: Counterexample-driven synthesis for probabilistic program sketches. In: FM. LNCS, vol. 11800, pp. 101–120. Springer (2019). https://doi.org/10.1007/978-3-030-30942-8_8
Chen, T., Forejt, V., Kwiatkowska, M.Z., Parker, D., Simaitis, A.: Automatic verification of competitive stochastic systems. Formal Methods Syst. Des. 43(1), 61–92 (2013). DOI: 10.1007/s10703-013-0183-7
Courtney, T., Gaonkar, S., Keefe, K., Rozier, E., Sanders, W.H.: Möbius 2.3: an extensible tool for dependability, security, and performance evaluation of large and complex system models. In: DSN, pp. 353–358. IEEE Computer Society (2009). https://doi.org/10.1109/DSN.2009.5270318
D’Argenio, P.R., Hartmanns, A., Legay, A., Sedwards, S.: Statistical approximation of optimal schedulers for probabilistic timed automata. In: iFM. LNCS, vol. 9681, pp. 99–114. Springer (2016). https://doi.org/10.1007/978-3-319-33693-0_7
D’Argenio, P.R., Hartmanns, A., Sedwards, S.: Lightweight statistical model checking in nondeterministic continuous time. In: ISoLA. LNCS, vol. 11245, pp. 336–353. Springer (2018). https://doi.org/10.1007/978-3-030-03421-4_22
D’Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G.: Reduction and refinement strategies for probabilistic analysis. In: PAPM-PROBMIV. LNCS, vol. 2399, pp. 57–76. Springer (2002). https://doi.org/10.1007/3-540-45605-8_5
Dehnert, C., Jansen, N., Wimmer, R., Ábrahám, E., Katoen, J.P.: Fast debugging of PRISM models. In: ATVA. LNCS, vol. 8837, pp. 146–162. Springer (2014). https://doi.org/10.1007/978-3-319-11936-6_11
Dehnert, C., et al.: PROPhESY: A PRObabilistic ParamEter SYnthesis tool. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 214–231. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21690-4_13
Dehnert, C., Junges, S., Katoen, J.P., Volk, M.: A Storm is coming: a modern probabilistic model checker. In: CAV. LNCS, vol. 10427, pp. 592–600. Springer (2017). https://doi.org/10.1007/978-3-319-63390-9_31
Delgrange, F., Katoen, J.P., Quatmann, T., Randour, M.: Simple strategies in multi-objective MDPs. In: TACAS. LNCS, vol. 12078, pp. 346–364. Springer (2020). https://doi.org/10.1007/978-3-030-45190-5_19
van Dijk, T., Hahn, E.M., Jansen, D.N., Li, Y., Neele, T., Stoelinga, M., Turrini, A., Zhang, L.: A comparative study of BDD packages for probabilistic symbolic model checking. In: SETTA. LNCS, vol. 9409, pp. 35–51. Springer (2015). https://doi.org/10.1007/978-3-319-25942-0_3
Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351. IEEE Computer Society (2010). https://doi.org/10.1109/LICS.2010.41
Etessami, K., Kwiatkowska, M.Z., Vardi, M.Y., Yannakakis, M.: Multi-objective model checking of Markov decision processes. Logic. Methods Comput. Sci. 4(4) (2008). https://doi.org/10.2168/LMCS-4(4:8)2008
Feng, Y., Hahn, E.M., Turrini, A., Ying, S.: Model checking omega-regular properties for quantum Markov chains. In: CONCUR. LIPIcs, vol. 85, pp. 35:1–35:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017). https://doi.org/10.4230/LIPIcs.CONCUR.2017.35
Fu, C., Turrini, A., Huang, X., Song, L., Feng, Y., Zhang, L.: Model checking probabilistic epistemic logic for probabilistic multiagent systems. In: IJCAI, pp. 4757–4763. ijcai.org (2018). https://doi.org/10.24963/ijcai.2018/661
Gainer, P., Hahn, E.M., Schewe, S.: Accelerated model checking of parametric Markov chains. In: ATVA. LNCS, vol. 11138, pp. 300–316. Springer (2018). https://doi.org/10.1007/978-3-030-01090-4_18
Gordon, A.D., Henzinger, T.A., Nori, A.V., Rajamani, S.K.: Probabilistic programming. In: FOSE, pp. 167–181. ACM (2014). https://doi.org/10.1145/2593882.2593900
Gros, T.P.: Markov automata taken by Storm. Master’s thesis, Saarland University, Germany (2018)
Guck, D., Hatefi, H., Hermanns, H., Katoen, J.P., Timmer, M.: Modelling, reduction and analysis of Markov automata. In: QEST. LNCS, vol. 8054, pp. 55–71. Springer (2013). https://doi.org/10.1007/978-3-642-40196-1_5
Haddad, S., Monmege, B.: Reachability in MDPs: Refining convergence of value iteration. In: RP. LNCS, vol. 8762, pp. 125–137. Springer (2014). https://doi.org/10.1007/978-3-319-11439-2_10
Haddad, S., Monmege, B.: Interval iteration algorithm for MDPs and IMDPs. Theor. Comput. Sci. 735, 111–131 (2018). https://doi.org/10.1016/j.tcs.2016.12.003
Hahn, E.M., Hartmanns, A.: A comparison of time- and reward-bounded probabilistic model checking techniques. SETTA. LNCS 9984, 85–100 (2016). https://doi.org/10.1007/978-3-319-47677-3_6
Hahn, E.M., Hartmanns, A., Hensel, C., Klauck, M., Klein, J., Kretínský, J., Parker, D., Quatmann, T., Ruijters, E., Steinmetz, M.: The 2019 comparison of tools for the analysis of quantitative formal models (QComp 2019 competition report). In: TACAS: TOOLympics. LNCS, vol. 11429, pp. 69–92. Springer (2019). https://doi.org/10.1007/978-3-030-17502-3_5
Hahn, E.M., Hartmanns, A., Hermanns, H., Katoen, J.P.: A compositional modelling and analysis framework for stochastic hybrid systems. Formal Methods Syst. Des. 43(2), 191–232 (2013). DOI: 10.1007/s10703-012-0167-z
Hahn, E.M., Hashemi, V., Hermanns, H., Lahijanian, M., Turrini, A.: Multi-objective robust strategy synthesis for interval MDPs. In: QEST. LNCS, vol. 10503, pp. 207–223. Springer (2017). https://doi.org/10.1007/978-3-319-66335-7_13
Hahn, Ernst Moritz, Hashemi, Vahid, Hermanns, Holger, Turrini, Andrea: Exploiting Robust Optimization for Interval Probabilistic Bisimulation. In: Agha, Gul, Van Houdt, Benny (eds.) QEST 2016. LNCS, vol. 9826, pp. 55–71. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-43425-4_4
Hahn, E.M., Li, G., Schewe, S., Zhang, L.: Lazy determinisation for quantitative model checking. CoRR abs/1311.2928 (2013). arxiv.org/abs/1311.2928
Hahn, E.M., Li, Y., Schewe, S., Turrini, A., Zhang, L.: iscasMc: a web-based probabilistic model checker. In: FM. LNCS, vol. 8442, pp. 312–317. Springer (2014). https://doi.org/10.1007/978-3-319-06410-9_22
Hahn, E.M., Schewe, S., Turrini, A., Zhang, L.: A simple algorithm for solving qualitative probabilistic parity games. In: CAV. LNCS, vol. 9780, pp. 291–311. Springer (2016). https://doi.org/10.1007/978-3-319-41540-6_16
Hartmanns, A., Hermanns, H.: The modest toolset: an integrated environment for quantitative modelling and verification. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 593–598. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_51
Hartmanns, A., Hermanns, H.: Explicit model checking of very large MDP using partitioning and secondary storage. In: ATVA. LNCS, vol. 9364, pp. 131–147. Springer (2015). https://doi.org/10.1007/978-3-319-24953-7_10
Hartmanns, A., Junges, S., Katoen, J.P., Quatmann, T.: Multi-cost bounded reachability in MDP. In: TACAS. LNCS, vol. 10806, pp. 320–339. Springer (2018). https://doi.org/10.1007/978-3-319-89963-3_19
Hartmanns, A., Kaminski, B.L.: Optimistic value iteration. In: CAV. LNCS, vol. 12225, pp. 488–511. Springer (2020). https://doi.org/10.1007/978-3-030-53291-8_26
Hartmanns, A., Klauck, M.: The 2020 Comparison of Tools for the Analysis of Quantitative Formal Models: Results and Reproduction. Zenodo (2020). https://doi.org/10.5281/zenodo.3965313
Hartmanns, A., Klauck, M., Parker, D., Quatmann, T., Ruijters, E.: The quantitative verification benchmark set. In: TACAS. LNCS, vol. 11427, pp. 344–350. Springer (2019). https://doi.org/10.1007/978-3-030-17462-0_20
Hartmanns, A., Sedwards, S., D’Argenio, P.R.: Efficient simulation-based verification of probabilistic timed automata. In: Winter Simulation Conference, pp. 1419–1430. IEEE (2017). https://doi.org/10.1109/WSC.2017.8247885
Hensel, C., Junges, S., Katoen, J.P., Quatmann, T., Volk, M.: The probabilistic model checker Storm. CoRR abs/2002.07080 (2020). arxiv.org/abs/2002.07080
Jansen, D.N.: Understanding Fox and Glynn’s “Computing Poisson probabilities”. CTIT technical report series (2011)
Junges, S., et al.: Parameter synthesis for Markov models. CoRR abs/1903.07993 (2019). arxiv.org/abs/1903.07993
Kelmendi, E., Krämer, J., Kretínský, J., Weininger, M.: Value iteration for simple stochastic games: Stopping criterion and learning algorithm. In: CAV. LNCS, vol. 10981, pp. 623–642. Springer (2018). https://doi.org/10.1007/978-3-319-96145-3_36
Klauck, M., Steinmetz, M., Hoffmann, J., Hermanns, H.: Compiling probabilistic model checking into prob. planning. In: ICAPS, pp. 150–154. AAAI Press (2018)
Klauck, M., Steinmetz, M., Hoffmann, J., Hermanns, H.: Bridging the gap between probabilistic model checking and probabilistic planning: Survey, compilations, and empirical comparison. J. Artif. Intell. Res. 68, 247–310 (2020). https://doi.org/10.1613/jair.1.11595
Kolobov, A., Mausam, Weld, D.S., Geffner, H.: Heuristic search for generalized stochastic shortest path MDPs. In: ICAPS. AAAI Press (2011)
Kwiatkowska, M.Z., Norman, G., Parker, D.: Stochastic games for verification of probabilistic timed automata. In: FORMATS. LNCS, vol. 5813, pp. 212–227. Springer (2009). https://doi.org/10.1007/978-3-642-04368-0_17
Kwiatkowska, M.Z., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: CAV. LNCS, vol. 6806, pp. 585–591. Springer (2011). https://doi.org/10.1007/978-3-642-22110-1_47
Kwiatkowska, M.Z., Norman, G., Parker, D.: The PRISM benchmark suite. In: QEST, pp. 203–204. IEEE Computer Society (2012). https://doi.org/10.1109/QEST.2012.14
Kwiatkowska, M.Z., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods Syst. Des. 29(1), 33–78 (2006). DOI: 10.1007/s10703-006-0005-2
Kwiatkowska, M.Z., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282(1), 101–150 (2002). https://doi.org/10.1016/S0304-3975(01)00046-9
Legay, A., Sedwards, S., Traonouez, L.M.: Scalable verification of Markov decision processes. In: WS-FMDS at SEFM. LNCS, vol. 8938, pp. 350–362. Springer (2014). https://doi.org/10.1007/978-3-319-15201-1_23
Lewis, E., Böhm, F.: Monte Carlo simulation of Markov unreliability models. Nucl. Eng. Design 77(1), 49–62 (1984). https://doi.org/10.1016/0029-5493(84)90060-8
Li, Y., Liu, W., Turrini, A., Hahn, E.M., Zhang, L.: An efficient synthesis algorithm for parametric Markov chains against linear time properties. CoRR abs/1605.04400 (2016)
de Moura, L.M., Bjørner, N.: Z3: An efficient SMT solver. In: TACAS. LNCS, vol. 4963, pp. 337–340. Springer (2008). https://doi.org/10.1007/978-3-540-78800-3_24
Neupane, T., Myers, C.J., Madsen, C., Zheng, H., Zhang, Z.: STAMINA: stochastic approximate model-checker for infinite-state analysis. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 540–549. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_31
Neupane, T., Zhang, Z., Madsen, C., Zheng, H., Myers, C.J.: Approximation techniques for stochastic analysis of biological systems. In: Automated Reasoning for Systems Biology and Medicine, Computational Biology, vol. 30, pp. 327–348. Springer (2019). https://doi.org/10.1007/978-3-030-17297-8_12
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Statistics, Wiley (1994). https://doi.org/10.1002/9780470316887
Quatmann, T., Junges, S., Katoen, J.P.: Markov automata with multiple objectives. In: CAV. LNCS, vol. 10426, pp. 140–159. Springer (2017). https://doi.org/10.1007/978-3-319-63387-9_7
Quatmann, T., Katoen, J.P.: Sound value iteration. In: CAV. LNCS, vol. 10981, pp. 643–661. Springer (2018). https://doi.org/10.1007/978-3-319-96145-3_37
Reijsbergen, D., de Boer, P.T., Scheinhardt, W.R.W., Juneja, S.: Path-ZVA: general, efficient, and automated importance sampling for highly reliable Markovian systems. ACM Trans. Model. Comput. Simul. 28(3), 22:1–22:25 (2018). https://doi.org/10.1145/3161569
Ruijters, E., et al.: FFORT: a benchmark suite for fault tree analysis. In: ESREL (2019). https://doi.org/10.3850/978-981-11-2724-3_0641-cd
Ruijters, E., Reijsbergen, D., de Boer, P.T., Stoelinga, M.: Rare event simulation for dynamic fault trees. Reliab. Eng. Syst. Saf. 186, 220–231 (2019). DOI: 10.1016/j.ress.2019.02.004
Spel, J., Junges, S., Katoen, J.P.: Are parametric Markov chains monotonic? In: ATVA. LNCS, vol. 11781, pp. 479–496. Springer (2019). https://doi.org/10.1007/978-3-030-31784-3_28
Steinmetz, M., Hoffmann, J., Buffet, O.: Goal probability analysis in probabilistic planning: Exploring and enhancing the state of the art. J. Artif. Intell. Res. 57, 229–271 (2016). https://doi.org/10.1613/jair.5153
Sullivan, K.J., Dugan, J.B., Coppit, D.: The Galileo fault tree analysis tool. In: FTCS, pp. 232–235. IEEE Computer Society (1999). https://doi.org/10.1109/FTCS.1999.781056
Volk, M., Junges, S., Katoen, J.P.: Fast dynamic fault tree analysis by model checking techniques. IEEE Trans. Ind. Informatics 14(1), 370–379 (2018). DOI: 10.1109/TII.2017.2710316
Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. Int. J. Softw. Tools Technol. Transf. 8(3), 216–228 (2006). https://doi.org/10.1007/s10009-005-0187-8
Younes, H.L.S., Littman, M.L., Weissman, D., Asmuth, J.: The first probabilistic track of the International Planning Competition. J. Artif. Intell. Res. 24, 851–887 (2005). DOI: 10.1613/jair.1880
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Budde, C.E. et al. (2021). On Correctness, Precision, and Performance in Quantitative Verification. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Tools and Trends. ISoLA 2020. Lecture Notes in Computer Science(), vol 12479. Springer, Cham. https://doi.org/10.1007/978-3-030-83723-5_15
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