As Cheap as Possible: Effcient Cost-Optimal Reachability for Priced Timed Automata

  • Kim Larsen
  • Gerd Behrmann
  • Ed Brinksma
  • Ansgar Fehnker
  • Thomas Hune
  • Paul Pettersson
  • Judi Romijn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2102)


In this paper we present an algorithm for efficiently computing optimal cost of reaching a goal state in the model of Linearly Priced Timed Automata (LPTA). The central contribution of this paper is a priced extension of so-called zones. This, together with a notion of facets of a zone, allows the entire machinery for symbolic reachability for timed automata in terms of zones to be lifted to cost-optimal reachability using priced zones. We report on experiments with a cost-optimizing extension of Uppaal on a number of examples.


Schedule Problem Model Check Symbolic Execution Target Time Symbolic State 
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.


  1. AC91.
    D. Applegate and W. Cook. A Computational Study of the Job-Shop Scheduling Problem. OSRA Journal on Computing 3, pages 149–156, 1991.zbMATHGoogle Scholar
  2. ACJYK96.
    P. Abdulla, K. Cerans, B. Jonsson, and T. Yih-Kuen. General decidability theorems for infinite-state systems, 1996.Google Scholar
  3. AD90.
    R. Alur and D. Dill. Automata for Modelling Real-Time Systems. In Proc. of Int. Colloquium on Algorithms, Languages and Programming, number 443 in Lecture Notes in Computer Science, pages 322–335, July 1990.Google Scholar
  4. AJ94.
    P. Abdulla and B. Jonsson. Undecidability of verifying programs with unreliable channels. In Proc. 21st Int. Coll. Automata, Languages, and Programming (ICALP’94), volume 820 of LNCS, 1994.Google Scholar
  5. ATP.
    R. Alun, S. La Torre, and G. J. Pappas. Optimal paths in weighted timed automata. To appear in HSCC2001.Google Scholar
  6. BDM+98.
    M. Bozga, C. Daws, O. Maler, A. Olivero, S. Tripakis, and S. Yovine. Kronos: A Model-Checking Tool for Real-Time Systems. In Proc. of the 10th Int. Conf. on Computer Aided Verification, number 1427 in Lecture Notes in Computer Science, pages 546–550. Springer-Verlag, 1998.CrossRefGoogle Scholar
  7. BFH+.
    G. Behrmann, A. Fehnker, T. Hune, K.G. Larsen, P. Pettersson, and J. Romijn. Efficient guiding towards cost-optimality in uppaal. To appear in Proceedings of TACAS’2001.Google Scholar
  8. BFH+01.
    _G. Behrmann, A. Fehnker, T. Hune, K. G. Larsen, P. Pettersson, J. Romijn, and F. Vaandrager. Minimum-Cost Reachability for Priced Timed Automata. To appear in Proceedings of HSCC2001, 2001.Google Scholar
  9. BKA00.
    J.E. Beasley, M. Krishnamoorthy, and D. Abramson. Scheduling Aircraft Landings-The Static Case. Transportation Science, 34(2):180–197, 2000.zbMATHCrossRefGoogle Scholar
  10. BM00.
    Ed Brinksma and Angelika Mader. Verification and optimization of a plc control schedule. In Proceedings of the 7th SPIN Workshop, volume 1885 of Lecture Notes in Computer Science. Springer Verlag, 2000.Google Scholar
  11. Cer94.
    K. Cerans. Deciding properties of integral relational automata. In Proceedings of ICALP 94, volume 820 of LNCS, 1994.Google Scholar
  12. Dil89.
    D. Dill. Timing Assumptions and Verification of Finite-State Concurrent Systems. In J. Sifakis, editor, Proc. of Automatic Verification Methods for Finite State Systems, number 407 in Lecture Notes in Computer Science, pages 197–212. Springer-Verlag, 1989.Google Scholar
  13. Don01.
    Jack J. Dongarra. Performance of Various Computers Using Standard Linear Equations Software. Technical Report CS-89-85, Computer Science Department, University of Tennessee, 2001. An up-to-date version of this report can be found at
  14. Feh99.
    A. Fehnker. Scheduling a steel plant with timed automata. In Proceedings of the 6th International Conference on Real-Time Computing Systems and Applications (RTCSA99), pages 280–286. IEEE Computer Society, 1999.Google Scholar
  15. FS98.
    A. Finkel and P. Schnoebelen. Fundamental structures in well-structured infinite transition systems. In Proc. 3rd Latin American Theoretical Informatics Symposium (LATIN’98), volume 1380 of LNCS, 1998.Google Scholar
  16. FS01.
    A. Finkel and Ph. Schnoebelen. Well structured transition systems everywhere. Theoretical Computer Science, 256(1-2):64–92, 2001.CrossRefMathSciNetGoogle Scholar
  17. HHWT97.
    T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: AModel Checker for Hybird Systems. In Orna Grumberg, editor, Proc. of the 9th Int. Conf. on Computer Aided Verification, number 1254 in Lecture Notes in Computer Science, pages 460–463. Springer-Verlag, 1997.Google Scholar
  18. Hig52.
    G. Higman. Ordering by divisibility in abstract algebras. Proc. of the London Math. Soc., 2:326–336, 1952.zbMATHCrossRefMathSciNetGoogle Scholar
  19. HLP00.
    T. Hune, K.G. Larsen, and P. Pettersson. Guided Synthesis of Control Programs Using Uppaal. In Ten H. Lai, editor, Proc. of the IEEE ICDCS International Workshop on Distributed Systems Verification and Validation, pages E15–E22. IEEE Computer Society Press, April 2000.Google Scholar
  20. LLPY97.
    Fredrik Larsson, Kim G. Larsen, Paul Pettersson, and Wang Yi. Efficient Verification of Real-Time Systems: Compact Data Structures and State-Space Reduction. In Proc. of the 18th IEEE Real-Time Systems Symposium, pages 14–24. IEEE Computer Society Press, December 1997.Google Scholar
  21. LPY97.
    K.G. Larsen, P. Pettersson, and W. Yi. Uppaal in a Nutshell. Int. Journal on Software Tools for Technology Transfer, 1(1-2):134–152, October 1997.zbMATHCrossRefGoogle Scholar
  22. Mil89.
    R. Milner. Communication and Concurrency. Prentice Hall, Englewood Cliffs, 1989.zbMATHGoogle Scholar
  23. NY99.
    P. Niebert and S. Yovine. Computing optimal operation schemes for multi batch operation of chemical plants. VHS deliverable, May 1999. Draft.Google Scholar
  24. RB98.
    T.C. Ruys and E. Brinksma. Experience with Literate Programming in the Modelling and Validation of Systems. In Bernhard Steffen, editor, Proceedings of the Fourth International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’98), number 1384 in Lecture Notes in Computer Science (LNCS), pages 393–408, Lisbon, Portugal, April 1998. Springer-Verlag, Berlin.CrossRefGoogle Scholar
  25. Rok93.
    T.G. Rokicki. Representing and Modeling Digital Circuits. PhD thesis, Stanford University, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kim Larsen
    • 1
    • 2
  • Gerd Behrmann
    • 1
  • Ed Brinksma
    • 2
  • Ansgar Fehnker
    • 4
  • Thomas Hune
    • 3
  • Paul Pettersson
    • 5
  • Judi Romijn
    • 4
  1. 1.Basic Research in Computer ScienceAalborg UniversityAalborg
  2. 2.Department of Computer SystemsUniversity of TwenteUK
  3. 3.Basic Research in Computer ScienceAarhus UniversityAarhus
  4. 4.University of NijmegenComputing Science InstituteNijmegen
  5. 5.Department of Information TechnologyUppsala UniversityUppsala

Personalised recommendations