Abstract
In this paper we present an algorithm for efficiently computing the minimum cost of reaching a goal state in the model of Uniformly Priced Timed Automata (UPTA). This model can be seen as a submodel of the recently suggested model of linearly priced timed automata, which extends timed automata with prices on both locations and transitions. The presented algorithm is based on a symbolic semantics of UTPA, and an efficient representation and operations based on difference bound matrices. In analogy with Dijkstra’s shortest path algorithm, we show that the search order of the algorithm can be chosen such that the number of symbolic states explored by the algorithm is optimal, in the sense that the number of explored states can not be reduced by any other search order. We also present a number of techniques inspired by branch-and-bound algorithms which can be used for limiting the search space and for quickly finding near-optimal solutions.
The algorithm has been implemented in the verification tool Uppaal. When applied on a number of experiments the presented techniques reduced the explored state-space with up to 90%.
This work is partially supported by the European Community Esprit-LTR Project 26270 VHS (Verification of Hybrid systems).
On sabbatical from Basic Research in Computer Science, Aalborg University.
Research supported by Netherlands Organization for Scientific Research (NWO) under contract SION 612-14-004.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
D. Applegate and W. Cook. A Computational Study of the Job-Shop Scheduling Problem. OSRA Journal on Computing 3, pages 149–156, 1991.
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.
G. Behrmann, A. Fehnker, T. Hune, K. G. Larsen, P. Pettersson, J. Romijn, and F. Vaandrager. Minimum-Cost Reachability for Priced Timed Automata. Accepted for Hybrid Systems: Computation and Control, 2001.
P. Brucker, B. Jurisch, and B. Sievers. Code of a Branch & Bound Algorithm for the Job Shop Problem. Available at url http://www.mathematik.uni-osnabrueck.de/research/OR/,1995.
R. Boel and G. Stremersch. Report for VHS: Timed Petri Net Model of Steel Plant at SIDMAR. Technical report, SYSTeMS Group, University Ghent, 1999.
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.
A. Fehnker. Bounding and heuristics in forward reachability algorithms. Technical Report CSI-R0002, Computing Science Institute Nijmegen, 1999.
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.
T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model 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.
T. Hune, K. G. Larsen, and P. Pettersson. Guided synthesis of control programs using UPPAAL for VHS case study 5. VHS deliverable, 1999.
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.
K. G. Larsen, P. Pettersson, and W. Yi. Diagnostic Model-Checking for Real-Time Systems. In Proc. of Workshop on Verification and Control of Hybrid Systems III, number 1066 in Lecture Notes in Computer Science, pages 575–586. Springer-Verlag, October 1995.
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.
P. Niebert, S. Tripakis, and S. Yovine. Minimum-time reachability for timed automata. In IEEE Mediteranean Control Conference, 2000. Accepted for publication.
P. Niebert and S. Yovine. Computing optimal operation schemes for multi batch operation of chemical plants. VHS deliverable, May 1999. Draft.
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.
F. Reffel and S. Edelkamp. Error Detection with Directed Symbolic Model Checking. In Proc. of Formal Methods, volume 1708 of Lecture Notes in Computer Science, pages 195–211. Springer-Verlag, 1999.
T. G. Rokicki. Representing and Modeling Digital Circuits. PhD thesis, Stanford University, 1993.
M. Stobbe. Results on scheduling the sidmar steel plant using constraint programming. Internal report, 2000.
F. Vaandrager. Analysis of a biphase mark protocol with Uppaal. to appear, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Behrmann, G., Fehnker, A., Hune, T., Larsen, K., Pettersson, P., Romijn, J. (2001). Efficient Guiding Towards Cost-Optimality in UPPAAL. In: Margaria, T., Yi, W. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2001. Lecture Notes in Computer Science, vol 2031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45319-9_13
Download citation
DOI: https://doi.org/10.1007/3-540-45319-9_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41865-8
Online ISBN: 978-3-540-45319-2
eBook Packages: Springer Book Archive