Abstract
Duration Calculus is a real-time interval logic which can be used to specify and reason about timing and logical constraints on discrete states in a dynamic system. It has been used to specify and verify designs for a number of real-time systems. This paper extends the Duration Calculus with notations to capture properties of piecewise continuous states. This is useful for reasoning about hybrid systems with a mixture of continuous and discrete states. The proof theory of Duration Calculus is extended such that results proven using mathematical analysis can be used freely in the logic. This provides a flexible interface to conventional control theory.
On leave from: Department of Computer Science Technical University of Denmark
Partially funded by ProCoS ESPRIT BRA 7071, by the Danish Technical Research Council RAPID, and by the Danish Natural Science Research Council
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
K.M. Hansen, A.P. Ravn, H. Rischel: Specifying and Verifying Requirements of Real-Time Systems, Proceedings of the ACM SIGSOFT '91 Conference on Software for Critical Systems, New Orleans, December 4–6, 1991, ACM Software Engineering Notes, vol. 15, no. 5, pp. 44–54, 1991.
M.R. Hansen, Zhou Chaochen: Semantics and Completeness of Duration Calculus, in J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (Eds.) Real-Time: Theory in Practice, REX Workshop, pp. 209–225, LNCS 600, 1992.
T. A. Henzinger, Z. Manna and A. Pnueli: Timed transition systems, in J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (Eds.) Real-Time: Theory in Practice, REX Workshop, pp. 226–251, LNCS 600, 1992.
R. Koymans: Specifying Real-Time Properties with Metric Temporal Logic, Real-Time Systems, 2, 4, pp. 255–299, Kluwer Academic Publishers, 1990.
David G. Luenberger: Introduction to Dynamic Systems. Theory, Models & Applications, Wiley, 1979.
O. Maler, Z. Manna and A. Pnueli: From Timed to Hybrid Systems, in J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (Eds.) Real-Time: Theory in Practice, REX Workshop, pp. 447–484, LNCS 600, 1992.
Z. Manna and A. Pnueli: The Temporal Logic of Reactive and Concurrent Systems, Springer Verlag, 1992.
K. Marzullo: Tolerating Failures of Continuous-Valued Sensors, Technical Rep. TR90-1156, Dept. Comp. Sc. Cornell University, Itacha, NY, USA.
B. Moszkowski: A Temporal Logic for Multilevel Reasoning about Hardware, IEEE Computer, 18, 2, pp. 10–19, 1985.
X. Nicollin, J. Sifakis and S. Yovine: From ATP to Timed Graphs and Hybrid Systems, in J. W. de Bakker, C. Huizing, W.-P. de Roever and G. Rozenberg (Eds.) Real-Time: Theory in Practice, REX Workshop, pp. 549–572, LNCS 600, 1992.
A. Pnueli and E. Harel: Applications of Temporal Logic to the Specification of Real-Time Systems (extended abstract), in M. Joseph (ed.) Proceedings of a Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, LNCS 331, pp. 84–98, Springer Verlag, 1988.
A.P. Ravn, H. Rischel: Requirements Capture for Embedded Real-Time Systems, Proc. IMACS-MCTS'91 Symp. Modelling and Control of Technological Systems, Vol 2, pp. 147–152, Villeneuve d'Ascq, France, 1991.
A.P. Ravn, H. Rischel and K.M. Hansen: Specifying and Verifying Requirements of Real-Time Systems, IEEE Trans. Softw. Eng. Vol. 19, No. 1, Jan. 1993, pp. 41–55.
J. U. Skakkebæk, A.P. Ravn, H. Rischel and Zhou Chaochen: Specification of embedded real-time systems, Proc. 4th Euromicro Workshop on Real-Time Systems, IEEE Press, pp 116–121, June 1992.
E.V. Sørensen, A.P. Ravn, H. Rischel: Control Program for a Gas Burner: Part 1: Informal Requirements, ProCoS Case Study 1, ProCoS Rep. ID/DTH EVS2, March 1990.
Zhou Chaochen, C.A.R. Hoare, A.P. Ravn: A Calculus of Durations, Information Processing Letters, 40, 5, pp. 269–276, 1991.
Zhou Chaochen, Li Xiaoshan: A Mean Value Calculus of Durations, UNI/IIST Report No. 5, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chaochen, Z., Ravn, A.P., Hansen, M.R. (1993). An extended duration calculus for hybrid real-time systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds) Hybrid Systems. HS HS 1992 1991. Lecture Notes in Computer Science, vol 736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57318-6_23
Download citation
DOI: https://doi.org/10.1007/3-540-57318-6_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57318-0
Online ISBN: 978-3-540-48060-0
eBook Packages: Springer Book Archive