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Formal Methods in System Design

, Volume 40, Issue 2, pp 122–146 | Cite as

Efficient emptiness check for timed Büchi automata

  • Frédéric Herbreteau
  • B. Srivathsan
  • Igor Walukiewicz
Article

Abstract

The Büchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the Büchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without an extra construction. An on-the-fly algorithm for the non-emptiness problem, using a non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.

Keywords

Timed automata Büchi accepting conditions Non-Zenoness On-the-fly algorithm 

References

  1. 1.
    Alur R, Dill DL (1994) A theory of timed automata. Theor Comput Sci 126(2):183–235 MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Alur R, Madhusudan P (2004) Decision problems for timed automata: A survey. In: Bernardo M, Corradini F (eds) Formal methods for the design of real-time systems, international school on formal methods for the design of computer, communication and software systems, SFM-RT 2004, Bertinoro, Italy, September 13–18, 2004, Revised Lectures. Lecture notes in computer science, vol 3185. Springer, Berlin, pp 1–24 Google Scholar
  3. 3.
    Behrmann G, Bouyer P, Larsen KG, Pelanek R (2006) Lower and upper bounds in zone-based abstractions of timed automata. Int J Softw Tools Technol Transf 8(3):204–215 CrossRefGoogle Scholar
  4. 4.
    Behrmann G, David A, Larsen KG, Haakansson J, Pettersson P, Yi W, Hendriks M (2006) Uppaal 4.0. In: Third international conference on the quantitative evaluation of systems (QEST 2006), 11–14 September 2006, Riverside, California, USA. IEEE Computer Society, Los Alamitos, pp 125–126 Google Scholar
  5. 5.
    Bérard B, Bouyer B, Petit A (2004) Analysing the pgm protocol with UPPAAL. Int J Prod Res 42(14):2773–2791 CrossRefGoogle Scholar
  6. 6.
    Berthomieu B, Menasche M (1983) An enumerative approach for analyzing time petri nets. In: IFIP Congress, pp 41–46 Google Scholar
  7. 7.
    Bouyer P (2003) Untameable timed automata! In: Alt H, Habib M (eds) STACS 2003, 20th annual symposium on theoretical aspects of computer science, Proceedings, Berlin, Germany, February 27–March 1, 2003. Lecture notes in computer science, vol 2607. Springer, Berlin, pp 620–631 Google Scholar
  8. 8.
    Bouyer P (2004) Forward analysis of updatable timed automata. Form Methods Syst Des 24(3):281–320 MATHCrossRefGoogle Scholar
  9. 9.
    Bowman H, Gómez R (2006) How to stop time stopping. Form Asp Comput 18(4):459–493 MATHCrossRefGoogle Scholar
  10. 10.
    Bozga M, Daws C, Maler O, Olivero A, Tripakis S, Yovine S (1998) Kronos: a model-checking tool for real-time systems. In: Hu AJ, Vardi MY (eds) Computer aided verification, 10th international conference, CAV ’98 Proceedings, Vancouver, BC, Canada, June 28–July 2, 1998. Lecture notes in computer science, vol 1427. Springer, Berlin, pp 546–550 CrossRefGoogle Scholar
  11. 11.
    Couvreur J-M (1999) On-the-fly verification of linear temporal logic. In: FM’99—formal methods, world congress on formal methods in the development of computing systems, Proceedings, vol I. Toulouse, France, September 20–24, 1999, p 1708 Google Scholar
  12. 12.
    Couvreur J-M, Duret-Lutz A, Poitrenaud D (2005) On-the-fly emptiness checks for generalized Büchi automata. In: Godefroid P (ed) Model checking software, 12th international SPIN workshop, Proceedings, San Francisco, CA, USA, August 22–24, 2005. Lecture notes in computer science, vol 3639. Springer, Berlin, pp 169–184 Google Scholar
  13. 13.
    Daws C, Tripakis S (1998) Model checking of real-time reachability properties using abstractions. In: Steffen B (ed) Tools and algorithms for construction and analysis of systems, 4th international conference, TACAS ’98, held as part of the European joint conferences on the theory and practice of software, ETAPS’98, Proceedings, Lisbon, Portugal, March 28–April 4, 1998. Lecture notes in computer science, vol 1384, pp 313–329 Google Scholar
  14. 14.
    Dill DL (1990) Timing assumptions and verification of finite-state concurrent systems. In: Sifakis J (ed) Automatic verification methods for finite state systems, international workshop, Proceedings, Grenoble, France, June 12–14, 1989. Lecture notes in computer science, vol 407. Springer, Berlin, pp 197–212 CrossRefGoogle Scholar
  15. 15.
    Gaiser A, Schwoon S (2009) Comparison of algorithms for checking emptiness on Büchi automata. In: Hilený P, Matyás V, Vojnar T (eds) Annual doctoral workshop on mathematical and engineering methods in computer science, MEMICS 2009, November 13–15, Prestige Hotel, Znojmo, Czech Republic, OASICS, vol 13. Schloss Dagstuhl—Leibniz-Zentrum fuer Informatik, Germany, 2009, pp 69–77 Google Scholar
  16. 16.
    Gómez R, Bowman H (2007) Efficient detection of Zeno runs in timed automata. In: Raskin J-F, Thiagarajan PS (eds) Formal modeling and analysis of timed systems, 5th international conference, FORMATS 2007, Proceedings, Salzburg, Austria, October 3–5, 2007. Lecture notes in computer science, vol 4763. Springer, Berlin, pp 195–210 CrossRefGoogle Scholar
  17. 17.
    Havelund K, Skou A, Larsen KG, Lund K (1997) Formal modeling and analysis of an audio/video protocol: An industrial case study using UPPAAL. In: Proceedings of the 18th IEEE real-time systems symposium (RTSS ’97), December 3–5, 1997, San Francisco, CA, USA. IEEE Computer Society, Los Alamitos, pp 2–13 Google Scholar
  18. 18.
    Herbreteau F, Srivathsan B (2010) Efficient on-the-fly emptiness check for timed Büchi automata. In: Bouajjani A, Chin W-N (eds) Automated technology for verification and analysis: 8th international symposium, ATVA 2010, Proceedings, Singapore, September 21–24, 2010. Lecture notes in computer science, vol 6252. Springer, Berlin, pp 218–232 CrossRefGoogle Scholar
  19. 19.
    Herbreteau F, Srivathsan B (2011) Coarse abstractions make Zeno behaviors difficult to detect. In: Katoen J-P, König B (eds) Concurrency theory, 22nd international conference, CONCUR 2011, Proceedings, Aachen, Germany, September 6–9, 2011. Lecture notes in computer science, vol 6901. Springer, Berlin, pp 92–107 CrossRefGoogle Scholar
  20. 20.
    Jessen JJ, Rasmussen JI, Larsen KG, David A (2007) Guided controller synthesis for climate controller using UPPAAL TiGA. In: Raskin J-F, Thiagarajan PS (eds) Formal modeling and analysis of timed systems, 5th international conference, FORMATS 2007, Proceedings, Salzburg, Austria, October 3–5, 2007. Lecture notes in computer science, vol 4763. Springer, Berlin, pp 227–240 CrossRefGoogle Scholar
  21. 21.
    Li G (2009) Checking timed Büchi automata emptiness using LU-abstractions. In: Ouaknine J, Vaandrager F (eds) Formal modeling and analysis of timed systems, 7th international conference, FORMATS 2009, Proceedings, Budapest, Hungary, September 14–16, 2009. Lecture notes in computer science, vol 5813. Springer, Berlin, pp 228–242 CrossRefGoogle Scholar
  22. 22.
    Schwoon S, Esparza J (2005) A note on on-the-fly verification algorithms. In: Halbwachs N, Zuck LD (eds) Tools and algorithms for the construction and analysis of systems, 11th international conference, TACAS 2005, held as part of the joint European conferences on theory and practice of software, ETAPS 2005, Proceedings, Edinburgh, UK, April 4–8, 2005. Lecture notes in computer science, vol 3440, pp 174–190 Google Scholar
  23. 23.
    Tripakis S (1999) Verifying progress in timed systems. In: Katoen J-P (ed) Formal methods for real-time and probabilistic systems, 5th international AMAST workshop, ARTS’99, Proceedings, Bamberg, Germany, May 26–28, 1999. Lecture notes in computer science, vol 1601. Springer, Berlin, pp 299–314 CrossRefGoogle Scholar
  24. 24.
    Tripakis S (2009) Checking timed Büchi emptiness on simulation graphs. ACM Trans Comput Logic, 10(3) Google Scholar
  25. 25.
    Tripakis S, Yovine S, Bouajjani A (2005) Checking timed Büchi automata emptiness efficiently. Form Methods Syst Des 26(3):267–292 MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Frédéric Herbreteau
    • 1
  • B. Srivathsan
    • 1
  • Igor Walukiewicz
    • 1
  1. 1.LaBRI, UMR 5800Univ. Bordeaux, CNRSTalenceFrance

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