Skip to main content
SpringerLink
Log in

Lipschitz Robustness of Timed I/O Systems

  • Conference paper
  • First Online:
Verification, Model Checking, and Abstract Interpretation (VMCAI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9583))

Abstract

We present the first study of robustness of systems that are both timed as well as reactive (I/O). We study the behavior of such timed I/O systems in the presence of uncertain inputs and formalize their robustness using the analytic notion of Lipschitz continuity: a timed I/O system is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions over timed words such as the timed version of the Manhattan distance and the Skorokhod distance. We consider two models of timed I/O systems — timed transducers and asynchronous sequential circuits. We show that K-robustness of timed transducers can be decided in polynomial space under certain conditions. For asynchronous sequential circuits, we reduce K-robustness w.r.t. timed Manhattan distances to K-robustness of discrete letter-to-letter transducers and show PSpace-completeness of the problem.

This research was supported in part by the European Research Council (ERC) under grant 267989 (QUAREM), by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE) and Z211-N23 (Wittgenstein Award), and by the National Science Centre (NCN), Poland under grant 2014/15/D/ST6/04543.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Madhusudan, P.: Decision problems for timed automata: a survey. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Bloem, R., Greimel, K., Henzinger, T., Jobstmann, B.: Synthesizing robust systems. In: Formal Methods in Computer Aided Design (FMCAD), pp. 85–92 (2009)

    Google Scholar 

  4. Bouyer, P., Brihaye, T., Bruyère, V., Raskin, J.-F.: On the optimal reachability problem on weighted timed automata. FMSD 31(2), 135–175 (2007)

    MATH  Google Scholar 

  5. Bouyer, P., Markey, N., Sankur, O.: Robustness in timed automata. In: Abdulla, P.A., Potapov, I. (eds.) RP 2013. LNCS, vol. 8169, pp. 1–18. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Černý, P., Henzinger, T.A., Radhakrishna, A.: Simulation distances. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 253–268. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Chaudhuri, S., Gulwani, S., Lublinerman, R.: Continuity analysis of programs. In: Principles of Programming Languages (POPL), pp. 57–70 (2010)

    Google Scholar 

  8. Chaudhuri, S., Gulwani, S., Lublinerman, R., Navidpour, S.: Proving programs robust. In: Foundations of Software Engineering (FSE), pp. 102–112 (2011)

    Google Scholar 

  9. Doyen, L., Henzinger, T.A., Legay, A., Ničković, D.: Robustness of sequential circuits. In: Application of Concurrency to System Design (ACSD), pp. 77–84 (2010)

    Google Scholar 

  10. Gupta, V., Henzinger, T.A., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  11. Henzinger, T.A.: Two challenges in embedded systems design: predictability and robustness. Philos. Trans. R. Soc. 366, 3727–3736 (2008)

    Article  Google Scholar 

  12. Henzinger, T.A., Otop, J., Samanta, R.: Lipschitz robustness of finite-state transducers. In: FSTTCS 2014, vol. 1, p. 431 (2014)

    Google Scholar 

  13. Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice Hall, Upper Saddle River (1996)

    MATH  Google Scholar 

  14. Krichen, M., Tripakis, S.: Conformance testing for real-time systems. Form. Methods Syst. Des. 34(3), 238–304 (2009)

    Article  MATH  Google Scholar 

  15. Lozano, A., Balcázar, J.L.: The complexity of graph problems for succinctly represented graphs. Graph-Theoretic Concepts in Computer Science. LNCS, vol. 411, pp. 277–286. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  16. Majumdar, R., Render, E., Tabuada, P.: A theory of robust omega-regular software synthesis. ACM Trans. Embed. Comput. Syst. 13, 1–27 (2013)

    Article  Google Scholar 

  17. Majumdar, R., Saha, I.: Symbolic robustness analysis. In: IEEE Real-Time Systems Symposium, pp. 355–363 (2009)

    Google Scholar 

  18. Samanta, R., Deshmukh, J.V., Chaudhuri, S.: Robustness analysis of networked systems. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 229–247. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Samanta, R., Deshmukh, J.V., Chaudhuri, S.: Robustness analysis of string transducers. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 427–441. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Stergiou, C., Tripakis, S., Matsikoudis, E., Lee, E.A.: On the verification of timed discrete-event models. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 213–227. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IST, Klosterneuburg, Austria

    Thomas A. Henzinger, Jan Otop & Roopsha Samanta

  2. University of Wrocław, Wrocław, Poland

    Jan Otop

Authors
  1. Thomas A. Henzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Otop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roopsha Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roopsha Samanta .

Editor information

Editors and Affiliations

  1. EPFL IC-DO, Lausanne, Switzerland

    Barbara Jobstmann

  2. Microsoft Research, Redmond, Washington, USA

    K. Rustan M. Leino

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Henzinger, T.A., Otop, J., Samanta, R. (2016). Lipschitz Robustness of Timed I/O Systems. In: Jobstmann, B., Leino, K. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2016. Lecture Notes in Computer Science(), vol 9583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49122-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-49122-5_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49121-8

  • Online ISBN: 978-3-662-49122-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation