By Felisa J. Vázquez-Abad (auth.), R. Boel, G. Stremersch (eds.)

*Discrete occasion platforms: research and Control* is the lawsuits of WODES2000 (the fifth Workshop on Discrete occasion structures, held in Ghent, Belgium, on August 21-23, 2000). This ebook offers a survey of the present state-of-the-art within the box of modeling, research and regulate synthesis of discrete occasion structures, lecture notes for a mini direction on sensitivity research for functionality evaluate of timed discrete occasion platforms, and forty eight rigorously chosen papers protecting all components of discrete occasion idea and crucial functions domain names. subject matters comprise automata concept and supervisory keep watch over (12); Petri internet dependent types for discrete occasion platforms, and their keep watch over synthesis (11); (max,+) and timed automata types (9); functions papers relating to scheduling, failure detection, and implementation of supervisory controllers (7); formal description of PLCs (6); and at last, stochastic types of discrete occasion structures (3).

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81(2):227-247. Park, D. (1981). Concurrency and automata on infinite sequences. In Proc. 5th GI Conf. on Th. , LNCS 104, pages 167-183. Springer-Verlag. Peled, D. (1994). Combining partial order reductions with on-the-fly model-checking. In Proc. of Worshop on Computer Aided Verification CA V'94, LNCS 818, pages 377-390. , and Le Borgne, M. (1999). Symbolic abstractions of automata and their application to the supervisory control problem. Research Report 1279, IRISA. Ramadge, P. J. and Wonham, W.

2. THE RESTRICTION PRINCIPLE The restriction consists in keeping suitable possible responses of the system in a given situation (x, y) to select the "good" possible extensions of the current behavior. The proposed method performs a static computation of the possible responses by delivering two constraints Co(X) and C(X, Y, K) interpreted as follows: Co(X) is a polynomial which denotes a set of suitable initial states, and C(X, Y, K) a set of suitable k's for a given situation (x, y). The restricted system is then simply obtained as 8' = (X,X', Y,K, T(X, Y,K,X') EB C(X, Y,K),!

The proposed method performs a static computation of the possible responses by delivering two constraints Co(X) and C(X, Y, K) interpreted as follows: Co(X) is a polynomial which denotes a set of suitable initial states, and C(X, Y, K) a set of suitable k's for a given situation (x, y). The restricted system is then simply obtained as 8' = (X,X', Y,K, T(X, Y,K,X') EB C(X, Y,K),! EB Co(X)). 3. ) and a set of states G, represented by a polynomial, say G(X). It is possible to compute symbolically the set of state for which a response can be chosen to reach G in one step (whatever the stimulus y is).