Article

Decidable Model Checking of Probabilistic Hybrid Automata

Author:

Jeremy SprostonAuthors Info & Claims

FTRTFT '00: Proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems

Pages 31 - 45

Published: 20 September 2000 Publication History

Abstract

Hybrid automata offer a framework for the description of systems with both discrete and continuous components, such as digital technology embedded in an analogue environment. Traditional uses of hybrid automata express choice of transitions purely in terms of nondeterminism, abstracting potentially significant information concerning the relative likelihood of certain behaviours. To model such probabilistic information, we present a variant of hybrid automata augmented with discrete probability distributions. We concentrate on restricted subclasses of the model in order to obtain decidable model checking algorithms for properties expressed in probabilistic temporal logics.

References

[1]

R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3-34, 1995.

[2]

R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126:183-235, 1994.

[3]

R. Alur, T. A. Henzinger, G. Lafferriere, and G. J. Pappas. Discrete abstractions of hybrid systems. To appear in Proceedings of the IEEE, 2000.

[4]

A. Aziz, V. Singhal, F. Balarin, R. Brayton, and A. Sangiovanni-Vincentelli. It usually works: the temporal logic of stochastic systems. In Proc. 7th CAV, volume 939 of Lecture Notes in Computer Science, pages 155-165. Springer-Verlag, 1995.

[5]

C. Baier. On algorithmic verification methods for probabilistic systems, 1998. Habilitation thesis, University of Mannheim.

[6]

C. Baier and M. Kwiatkowska. Model checking for a probabilistic branching time logic with fairness. Distributed Computing, 11:125-155, 1998.

[7]

A. Bianco and L. de Alfaro. Model checking of probabilistic and nondeterministic systems. In Proc. FST & TCS'95, volume 1026 of LNCS, pages 499-513. Springer-Verlag, 1995.

[8]

L. de Alfaro, M. Kwiatkowska, G. Norman, D. Parker, and R. Segala. Symbolic model checking of concurrent probabilistic processes using MTBDDs and the Kronecker representation. In Proc. TACAS'00, volume 1785 of LNCS, pages 395- 410. Springer-Verlag, 2000.

[9]

H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6(5):512-535, 1994.

[10]

T. A. Henzinger, B. Horowitz, and R. Majumdar. Rectangular hybrid games. In Proc. CONCUR'99, volume 1664 of LNCS, pages 320-335. Springer-Verlag, 1999.

[11]

T. A. Henzinger, B. Horowitz, R. Majumdar, and H. Wong-Toi. Beyond HYTECH: hybrid systems analysis using interval numerical methods. In Proc. HSCC'00, volume 1790 of LNCS, pages 130-144. Springer-Verlag, 2000.

[12]

T. A. Henzinger, P. Kopke, A. Puri, and P. Varaiya. What's decidable about hybrid automata? Journal of Computer and System Sciences, 57(1):94-124, 1998.

[13]

T. A. Henzinger and R. Majumdar. Symbolic model checking for rectangular hybrid systems. In Proc. TACAS'00, volume 1785 of LNCS, pages 142-156. Springer-Verlag, 2000.

[14]

J. Hu, J. Lygeros, and S. Sastry. Towards a theory of stochastic hybrid systems. In Proc. HSCC'00, volume 1790 of LNCS. Springer-Verlag, 2000.

[15]

B. Jonsson and K. G. Larsen. Specification and refinement of probabilistic processes. In Proc. 6th LICS, pages 266-279. IEEE Computer Society Press, 1991.

[16]

M. Kwiatkowska, G. Norman, R. Segala, and J. Sproston. Automatic verification of real-time systems with discrete probability distributions. To appear in Theoretical Computer Science, special issue on ARTS'99: Formal Methods for Real-time and Probabilistic Systems, 2000.

[17]

M. Kwiatkowska, G. Norman, R. Segala, and J. Sproston. Verifying quantitative properties of continuous probabilistic timed automata. In Proc. CONCUR'00, LNCS. Springer-Verlag, 2000.

[18]

G. Lafferriere, G. Pappas, and S. Yovine. A new class of decidable hybrid systems. In Proc. HSCC'99, volume 1569 of LNCS, pages 137-151. Springer-Verlag, 1999.

[19]

R. Milner. Communication and Concurrency. International Series in Computer Science. Prentice Hall, 1989.

[20]

A. Olivero, J. Sifakis, and S. Yovine. Using abstractions for the verification of linear hybrid systems. In Proc. 6th CAV, volume 818 of LNCS, pages 81-94. Springer-Verlag, 1994.

[21]

R. Segala and N. Lynch. Probabilistic simulations for probabilistic processes. Nordic Journal of Computing, 2(2):250-273, 1995.

Cited By

Huang CChen XLin WYang ZLi X(2017)Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier CertificatesACM Transactions on Embedded Computing Systems10.1145/312650816:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126508
Zhang HWu JLu JTang J(2016)Safety verification of finite real-time nonlinear hybrid systems using enhanced group preserving schemeCluster Computing10.1007/s10586-016-0652-z19:4(2189-2199)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10586-016-0652-z
Peng YWang SZhan NZhang L(2015)Extending Hybrid CSP with Probability and StochasticityProceedings of the First International Symposium on Dependable Software Engineering: Theories, Tools, and Applications - Volume 940910.1007/978-3-319-25942-0_6(87-102)Online publication date: 4-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-25942-0_6
Show More Cited By

Index Terms

Decidable Model Checking of Probabilistic Hybrid Automata
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Formal methods
        Model checking
2. Theory of computation
  1. Formal languages and automata theory
  2. Logic

Index terms have been assigned to the content through auto-classification.

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cover image Guide Proceedings

FTRTFT '00: Proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems

September 2000

302 pages

ISBN:3540410554

Editor:
Mathai Joseph

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 20 September 2000

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Cited By

Huang CChen XLin WYang ZLi X(2017)Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier CertificatesACM Transactions on Embedded Computing Systems10.1145/312650816:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126508
Zhang HWu JLu JTang J(2016)Safety verification of finite real-time nonlinear hybrid systems using enhanced group preserving schemeCluster Computing10.1007/s10586-016-0652-z19:4(2189-2199)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10586-016-0652-z
Peng YWang SZhan NZhang L(2015)Extending Hybrid CSP with Probability and StochasticityProceedings of the First International Symposium on Dependable Software Engineering: Theories, Tools, and Applications - Volume 940910.1007/978-3-319-25942-0_6(87-102)Online publication date: 4-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-25942-0_6
Hahn EHermanns HBelta CIvančić F(2013)Rewarding probabilistic hybrid automataProceedings of the 16th international conference on Hybrid systems: computation and control10.1145/2461328.2461375(313-322)Online publication date: 8-Apr-2013
https://dl.acm.org/doi/10.1145/2461328.2461375
Kwiatkowska M(2013)From software verification to `everyware' verificationComputer Science - Research and Development10.1007/s00450-013-0249-128:4(295-310)Online publication date: 1-Nov-2013
https://dl.acm.org/doi/10.1007/s00450-013-0249-1
Fränzle MHahn EHermanns HWolovick NZhang LCaccamo MFrazzoli EGrosu R(2011)Measurability and safety verification for stochastic hybrid systemsProceedings of the 14th international conference on Hybrid systems: computation and control10.1145/1967701.1967710(43-52)Online publication date: 12-Apr-2011
https://dl.acm.org/doi/10.1145/1967701.1967710
Zhang LShe ZRatschan SHermanns HHahn E(2010)Safety verification for probabilistic hybrid systemsProceedings of the 22nd international conference on Computer Aided Verification10.1007/978-3-642-14295-6_21(196-211)Online publication date: 15-Jul-2010
https://dl.acm.org/doi/10.1007/978-3-642-14295-6_21
Mutsuda YKato TYamane S(2005)Specification and verification techniques of embedded systems using probabilistic linear hybrid automataProceedings of the Second international conference on Embedded Software and Systems10.1007/11599555_34(346-360)Online publication date: 16-Dec-2005
https://dl.acm.org/doi/10.1007/11599555_34

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