Counter Automata for Parameterised Timing Analysis of Box-Based Systems

  • Christoph A. Herrmann
  • Kevin Hammond
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7177)


We present a new compositional approach for analysing the resource usage of reactive box-based systems, as exemplified by Hume. Our analysis deals with a key aspect of reactivity, namely determining the worst-case execution time between some external input event and the associated output event, taking into account repeated box iterations and the possible interactions between boxes in terms of input/output values. In order to achieve this, we capture the system behaviour by abstract interpretation, obtaining counter automata, finite state automata with additional counters that can be used to represent sizes/resource costs and control repetitions. These counter automata precisely capture cost information from the original box-based system, but in a way that is more abstract and therefore easier to analyse. The key contribution of this paper over previous work is that we are able to analyse box-based computations for cyclic systems whose costs may depend on some input parameters and in which the cost formulae are non-linear.


Abstract Interpretation State Automaton Abstract Domain Schedule Cycle WCET Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. Journal of Automated Reasoning 46(2), 161–203 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Annichini, A., Asarin, E., Bouajjani, A.: Symbolic Techniques for Parametric Reasoning About Counter and Clock Systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 419–434. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Bernat, G., Burns, A.: An approach to symbolic worst-case execution time analysis. In: 25th Workshop on Real-Time Programming, Palma, Spain (May 2000)Google Scholar
  5. 5.
    Bozga, M., Iosif, R., Lakhnech, Y.: Flat Parametric Counter Automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 577–588. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Bygde, S., Lisper, B.: Towards an automatic parametric WCET analysis. In: 8th Intl. Workshop on Worst-Case Execution Time (WCET) Analysis (2008); associated with ECRTS 2008Google Scholar
  7. 7.
    Chin, W.-N., Khoo, S.-C.: Calculating sized types. In: Partial Evaluation and Semantics-based Program Manipulation, pp. 62–72 (2000)Google Scholar
  8. 8.
    Coffman, J., Healy, C., Mueller, F., Whalley, D.: Generalizing parametric timing analysis. In: LCTES 2007, pp. 152–154 (2007)Google Scholar
  9. 9.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc. Principles of Programming Languages (POPL), pp. 238–252 (1977)Google Scholar
  10. 10.
    Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics. 2nd edition. Pearson Education (1994)Google Scholar
  11. 11.
    Hammond, K., Michaelson, G.J.: Hume: A Domain-Specific Language for Real-Time Embedded Systems. In: Pfenning, F., Macko, M. (eds.) GPCE 2003. LNCS, vol. 2830, pp. 37–56. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Hernández-Marin, S., Wallace, A.M., Gibson, G.J.: Bayesian analysis of LiDAR signals with multiple returns. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(12), 2170–2180 (2007)CrossRefGoogle Scholar
  13. 13.
    Herrmann, C.A., Bonenfant, A., Hammond, K., Jost, S., Loidl, H.-W., Pointon, R.: Automatic amortised worst-case execution time analysis. In: Rochange, C. (ed.) 7th Intl. Workshop on Worst-Case Execution Time (WCET) Analysis. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2007)Google Scholar
  14. 14.
    Hoffmann, J., Aehlig, K., Hofmann, M.: Multivariate Amortized Resource Analysis. In: 38th Symp. on Principles of Prog. Langs. (POPL 2011), pp. 357–370 (2011)Google Scholar
  15. 15.
    Hovland, D.: Regular Expressions with Numerical Constraints and Automata with Counters. In: Leucker, M., Morgan, C. (eds.) ICTAC 2009. LNCS, vol. 5684, pp. 231–245. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Jost, S., Hammond, K., Loidl, H.-W., Hofmann, M.: Static determination of quantitative resource usage for higher-order programs. In: Proc. Principles of Programming Languages, POPL (2010)Google Scholar
  17. 17.
    Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer (1999)Google Scholar
  18. 18.
    Penczek, F., Herhut, S., Grelck, C., Scholz, S.-B., Shafarenko, A., Barrière, R., Lenormand, E.: Parallel Signal Processing with S-Net. Procedia Computer Science 1(1), 2079–2088 (2010); ICCS 2010CrossRefGoogle Scholar
  19. 19.
    Schüle, T., Schneider, K.: Exact runtime analysis using automata-based symbolic simulations. In: Proc 1st ACM/IEEE Int. Conf. Formal Methods and Models for Co-Design (MEMOCODE 2003). IEEE Computer Society (2003)Google Scholar
  20. 20.
    Sipser, M.: Introduction to the Theory of Computation. PWS Publishing Company (1997)Google Scholar
  21. 21.
    Sperberg-McQueen, M.: Notes on finite state automata with counters (May 2004),
  22. 22.
    Valiant, L.G.: A bridging model for parallel computation. Communications of the ACM 33(8), 103–111 (1990)CrossRefGoogle Scholar
  23. 23.
    Wegbreit, B.: Mechanical program analysis. Communication of the ACM 18(9), 528–539 (1975)MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christoph A. Herrmann
    • 1
  • Kevin Hammond
    • 1
  1. 1.University of St. AndrewsScotland, UK

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