Abstract
In classical applied mathematics time is treated as an independent variable. The equations which govern the behaviour of a system enable one to determine, in principle, what happens at a given time. This approach has led to powerful techniques for calculating numerical quantities of interest in engineering. The temporal behaviour of reactive systems, however, is difficult to treat from this viewpoint and it has been customary to rely on logical rather than dynamic methods. In this paper we describe the theory of min-max functions, [6, 11, 15], which permits a dynamic approach to the time behaviour of a restricted class of reactive systems. Our main result is a proof of the Duality Conjecture for min-max functions of dimension 2.
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References
F. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat. Synchronization and Linearity. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, 1992.
S. M. Burns. Performance Analysis and Optimization of Asynchronous Circuits. PhD thesis, California Institute of Technology, 1990.
J. Campos, G. Chiola, and M. Silva. Ergodicity and throughput bounds of Petri nets with unique consistent firing count vector. IEEE Transactions on Software Engineering, 17 (2): 117–125, 1991.
R. A. Cuninghame-Green. Describing industrial processes with interference and approximating their steady-state behaviour. Operational Research Quarterly, 13 (1): 95–100, 1962.
R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley Publishing Company, Inc., 1989.
J. Gunawardena. Min-max functions. To appear in Discrete Event Dynamic Systems.
J. Gunawardena. The Muller unfolding. In preparation.
J. Gunawardena. A generalized event structure for the Muller unfolding of a safe net. In E. Best, editor, CONCUR’93–4th International Conference on Concurrency Theory, pages 278–292. Springer LNCS 715, 1993.
J. Gunawardena. Periodic behaviour in timed systems with |AND, OR~ causality. Part I: systems of dimension 1 and 2. Technical Report STAN-CS-93–1462, Department of Computer Science, Stanford University, February 1993.
J. Gunawardena. Timing analysis of digital circuits and the theory of min-max functions. In TAU’93, ACM International Workshop on Timing Issues in the Specification and Synthesis of Digital Systems, September 1993.
J. Gunawardena. Cycle times and fixed points of min-max functions. To appear in the Proceedings of the 11th International Conference on Analysis and Optimization of Systems, Sophia-Antipolis, France, June 1994.
R. M. Keller. A fundamental theorem of asynchronous parallel computation. In T. Y. Feng, editor, Parallel Processing, pages 102–112. Springer LNCS 24, 1975.
L. H. Landweber and E. L. Robertson. Properties of conflict-free and persistent Petri nets. Journal ACM, 25 (3): 352–364, 1978.
R. Milner. Communication and Concurrency. International Series in Computer Science. Prentice-Hall, 1989.
G. J. Olsder. Eigenvalues of dynamic max-min systems. Discrete Event Dynamic Systems, 1: 177–207, 1991.
T. Szymanski and N. Shenoy. Verifying clock schedules. In Digest of Technical Papers of the IEEE International Conference on Computer-Aided Design of Integrated Circuits, pages 124–131. IEEE Computer Society, 1992.
J. Vytopil, editor. Formal Techniques in Real-Time and Fault-Tolerant Systems. Springer LNCS 571, 1991.
G. Winskel. Event structures. In W. Brauer, W. Reisig, and G. Rozenberg, editors, Advances in Petri Nets. Springer LNCS 255, 1987.
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© 1994 Springer-Verlag Berlin Heidelberg
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Gunawardena, J. (1994). A Dynamic Approach to Timed Behaviour. In: Jonsson, B., Parrow, J. (eds) CONCUR ’94: Concurrency Theory. CONCUR 1994. Lecture Notes in Computer Science, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48654-1_17
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DOI: https://doi.org/10.1007/978-3-540-48654-1_17
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