Carina Da Silva
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Stochastic hybrid automata (SHA) are a powerful tool to evaluate the dependability and safety of critical infrastructures. However, the resolution of nondeterminism, which is present in many purely hybrid models, is often only implicitly considered in SHA. This article instead proposes algorithms for computing maximum and minimum reachability probabilities for singular automata with urgent transitions and random clocks that follow arbitrary continuous probability distributions. We borrow a well-known approach from hybrid systems reachability analysis, namely flowpipe construction, which is then extended to optimize nondeterminism in the presence of random variables. First, valuations of random clocks that ensure reachability of specific goal states are extracted from the computed flowpipes, and second, reachability probabilities are computed by integrating over these valuations. We compute maximum and minimum probabilities for history-dependent prophetic and non-prophetic schedulers using set-based methods. The implementation featuring the library HyPro and the complexity of the approach are discussed in detail. Two case studies featuring nondeterministic choices show the feasibility of the approach.
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- [1] . 2010. Approximate model checking of stochastic hybrid systems. European Journal of Control 16, 6 (2010), 624–641.Google Scholar
Cross Ref
- [2] . 1995. The algorithmic analysis of hybrid systems. Theoretical Computer Science 138 (1995), 3–34.Google ScholarDigital Library
- [3] . 2013. Transient analysis of networks of stochastic timed automata using stochastic state classes. In 10th Int. Conf. on Quantitative Evaluation of Systems (QEST’13) (LNCS), Vol. 8054. Springer, 355–371.Google Scholar
- [4] . 2014. Stochastic timed automata. Logical Methods in Computer Science 10, 4 (2014), 1–73.Google Scholar
- [5] . 2006. MODEST: A compositional modeling formalism for hard and softly timed systems. IEEE Transactions on Software Engineering 32, 10 (2006), 812–830.Google ScholarDigital Library
- [6] . 2018. A statistical model checker for nondeterminism and rare events. In 24th Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’18) (LNCS’18), Vol. 10806. Springer, 340–358.Google Scholar
- [7] . 2018. A hierarchy of scheduler classes for stochastic automata. In 21st Int. Conf. on Foundations of Software Science and Computation Structures (FoSSaCS’18) (LNCS’18), Vol. 10803. Springer, 384–402.Google Scholar
- [8] . 2005. A theory of stochastic systems part I: Stochastic automata. Information and Computation 203, 1 (2005), 1–38.Google ScholarDigital Library
- [9] . 2023. Maximizing reachability probabilities in rectangular automata with random clocks. In 17th Int. Symp. on Theoretical Aspects of Software Engineering (LNCS), Vol. 13931. Springer, 1–19.Google Scholar
- [10] . 1827. Analyse des Travaux de l’académie Royale des Sciences Pendant l’année 1824. Partie Mathématique (1827).Google Scholar
- [11] . 2011. Measurability and safety verification for stochastic hybrid systems. In 14th ACM Int. Conf. on Hybrid Systems: Computation and Control (HSCC’11). ACM, 43–52.Google Scholar
- [12] . 2005. PHAVer: Algorithmic verification of hybrid systems past HyTech. In 8th Int. Workshop on Hybrid Systems: Computation and Control (HSCC’05) (LNCS’05), Vol. 3414. Springer, 258–273.Google Scholar
- [13] . 2013. Analysis of a sewage treatment facility using hybrid petri nets. In 7th EAI Int. Conf. on Performance Evaluation Methodologies and Tools (VALUETOOLS’13). ICST, 165–174.Google Scholar
- [14] . 2009. Gnu Scientific Library Reference Manual. Network Theory Ltd.Google ScholarDigital Library
- [15] . 2014. Reachability and reward checking for stochastic timed automata. Electronic Communiations of the EASST 70 (2014).Google Scholar
- [16] . 2013. A compositional modelling and analysis framework for stochastic hybrid systems. Formal Methods in System Design 43, 2 (2013), 191–232.Google ScholarDigital Library
- [17] . 2000. The theory of hybrid automata. In Verification of Digital and Hybrid Systems.
NATO ASI Series , Vol. 170. Springer, 265–292.Google ScholarCross Ref - [18] . 1998. What’s decidable about hybrid automata? Journal of Computer and System Sciences 57, 1 (1998), 94–124.Google ScholarDigital Library
- [19] . 2005. Analysis of Zeno behaviors in a class of hybrid systems. IEEE Transactions on Automated Control 50, 3 (2005), 376–383.Google ScholarCross Ref
- [20] . 2020. Hpnmg: A C++ tool for model checking hybrid petri nets with general transitions. In 12th Int. NASA Formal Methods Symp. (NFM’20) (LNCS’20), Vol. 12229. Springer, 369–378.Google Scholar
- [21] . 2019. State-space construction of hybrid petri nets with multiple stochastic firings. In 16th Int. Conf. on Quantitative Evaluation of Systems (QEST’19) (LNCS’19), Vol. 11785. Springer, 182–199.Google Scholar
- [22] . 2021. State-space construction of hybrid petri nets with multiple stochastic firings. ACM Transactions on Modeling and Computer Simulation 31, 3 (2021), 1–37.Google ScholarDigital Library
- [23] . 2016. Coordinated charging strategies for plug-in electric vehicles to ensure a robust charging process. In 10th EAI Int. Conf. on Performance Evaluation Methodologies and Tools (VALUETOOLS’16). ICST.Google Scholar
- [24] . 2016. Energy storage in smart homes: Grid-convenience versus self-use and survivability. In 24th IEEE Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems. IEEE, 385–390.Google Scholar
- [25] . 2008. Computational methods for verification of stochastic hybrid systems. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 38, 2 (2008), 385–396.Google ScholarDigital Library
- [26] . 2000. Verifying quantitative properties of continuous probabilistic timed automata. In 11th Int. Conf. on Concurrency Theory (CONCUR’00) (LNCS’00), Vol. 1877. Springer, 123–137.Google Scholar
- [27] . 2021. Adaptive multidimensional integration: VEGAS enhanced. Journal of Computational Physics 439 (2021), 110386.
arxiv:2009.05112 [hep-ph, physics:physics] Google ScholarCross Ref - [28] . 1987. On the complexity of linear programming. In Advances in Economic Theory. Cambridge University Press, London, 225–268.Google Scholar
- [29] . 1936. Beitrage Zur Theorie Der Linearen Ungleichungen. Azriel.Google Scholar
- [30] . 2021. Learning optimal decisions for stochastic hybrid systems. In 19th ACM-IEEE Int. Conf. on Formal Methods and Models for System Design (MEMOCODE’21). ACM, 44–55.Google Scholar
- [31] . 2020. Classic and non-prophetic model checking for hybrid petri nets with stochastic firings. In 23rd ACM Int. Conf. on Hybrid Systems: Computation and Control (HSCC’20). ACM, 1–11.Google Scholar
- [32] . 2020. A transformation of hybrid petri nets with stochastic firings into a subclass of stochastic hybrid automata. In 12th Int. NASA Formal Methods Symp. (NFM’20) (LNCS), Vol. 12229. Springer, 381–400.Google Scholar
- [33] . 2021. Optimizing reachability probabilities for a restricted class of stochastic hybrid automata via flowpipe-construction. In 18th Int. Conf. on Quantitative Evaluation of Systems (QEST’21) (LNCS), Vol. 12846. Springer, Cham, 435–456.Google Scholar
- [34] . 2006. A stochastic approximation method for reachability computations. In Stochastic Hybrid Systems: Theory and Safety Critical Applications.
LNCIS , Vol. 337. Springer, 107–139.Google Scholar - [35] . 2019. State Set Representations and Their Usage in the Reachability Analysis of Hybrid Systems. Dissertation. RWTH Aachen University. http://publications.rwth-aachen.de/record/767529Google Scholar
- [36] . 2017. HyPro: A C++ library of state set representations for hybrid systems reachability analysis. In 9th Int. NASA Formal Methods Symp. (NFM’17) (LNCS), Vol. 10227. Springer, Cham, 288–294.Google Scholar
- [37] . 2015. FAUST2: Formal abstractions of uncountable-STate STochastic processes. In 21st Int. Conf. on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’15) (LNCS), Vol. 9035. Springer, 272–286.Google Scholar
- [38] . 2000. Decidable model checking of probabilistic hybrid automata. In 6th Int. Symp. on Formal Techniques in Real-time and Fault-tolerant Systems (FTRTFT’00) (LNCS), Vol. 1926. Springer, 31–45.Google Scholar
- [39] . 2012. Safety verification for probabilistic hybrid systems. European Journal of Control 18, 6 (2012), 572–587.Google ScholarCross Ref
- [40] . 1995. Lectures on Polytopes.
Graduate Texts in Mathematics , Vol. 152. Springer Science & Business Media.Google ScholarCross Ref
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