Abstract
This paper is to present an algorithm to decide whether a real-time system satisfies a set of invariants which are constructed from linear inequalities of integrated durations of system states. Real-time systems in the paper are taken to be real-time automata which set up for each of state transitions a lower time bound and an upper time bound. The satisfaction problem can be translated into a family of linear programming problems. The algorithm is, according to the invariants, to reduce the infinite family of linear programming problems to an equivalent one with only finite members, and then to solve each of linear programming problems efficiently. The algorithm is so simple that no prerequisite of linear programming theory is assumed.
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References
R. Alur, C. Courcoubetis, T. Henzinger, P-H Ho: Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems, in Hybrid Systems, LNCS 736, pp 209–229, R. L. Grossman, A. Nerode, A. P. Ravn and H. Rischel (eds.), Springer-Verlag, 1993
M. Engel, M. Kubica, J. Madey, D.J. Parnas, A.P. Ravn, A.J. van Schouwen: A Formal Approach to Computer Systems Requirements Documentation, in Hybrid Systems, LNCS 736, pp 452–474, R. L. Grossman, A. Nerode, A. P. Ravn and H. Rischel (eds.), Springer-Verlag, 1993
Y. Kesten, A. Pnueli, J. Sifakis, S. Yovine: Integration Graphs: A Class of Decidable Hybrid Systems, in Hybrid Systems, LNCS 736, pp 179–208, R. L. Grossman, A. Nerode, A. P. Ravn and H. Rischel (eds.), Springer-Verlag, 1993
S.C. Kleene: Representation of Events in Nerve Nets and Finite Automata, in Automata Studies, pp 3–41, C. Shannon and J. McCarthy (eds.), Princeton Univ. Press, Princeton, NJ, 1956
Z. Manna, A. Pnueli: Verifying Hybrid Systems, in Hybrid Systems, LNCS 736, pp 4–35, R. L. Grossman, A. Nerode, A. P. Ravn and H. Rischel (eds.), Springer-Verlag, 1993
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, K.M. Hansen: Specifying and Verifying Requirements of Real-Time Systems, IEEE Trans. Software Eng., Vol 19, No 1, pp 41–55, January 1993
J.U. SkakkebÆk, A.P. Ravn, H. Rischel, Zhou Chaochen: Specification of Embedded Real-Time Systems, Proc. 4th Euromicro Workshop on Real-Time Systems, IEEE Press, pp 116–121, June 1992
Zhou Chaochen, C.A.R. Hoare, A.P. Ravn: A Calculus of Durations, Information Processing Letter, 40, 5, pp. 269–276, 1991
Zhou Chaochen, Li Xiaoshan: A Mean-Value Duration Calculus, in A Classical Mind, Essays in Honour of C. A. R. Hoare, pp 431–451, A. W. Roscoe (ed.), Prentice Hall International, 1994
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Chaochen, Z., Jingzhong, Z., Lu, Y., Xiaoshan, L. (1994). Linear duration invariants. In: Langmaack, H., de Roever, WP., Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT ProCoS 1994 1994. Lecture Notes in Computer Science, vol 863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58468-4_161
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DOI: https://doi.org/10.1007/3-540-58468-4_161
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