New PDF release: 11th International Conference on Analysis and Optimization

extend to =¢,. In particular x =~ y stands for x -+ y where ~ stands for the empty string in I]*. It is possible to hide (or internalize) certain event transitions of an automaton A. For a subset I]o of E we let A. Eo where the latter is obtained from the former by replacing the labels of the edges of GA by the symbol r unless the label is in I] o. Let A be an automaton and let Q c_ QA. We define L(Q), the (prefix) closed language generated by Q, as follows : L(Q):={s6 I]*13q6 Q:q~} .

References [CW90] P. E. Wang,COCOLOG:A conditional observer and controller logic for finite machines, Proceeding of the 29th IEEE CDC, Hawaii, 1990, pp. M r . [CWe94] RE. Wei The hierarchical lattice of a finite machine, submitted for publication to System and Control Letters, Feb, 1994 A. Ginzburg, Algebraic Theory of Automata, Academic Press, New York, 1968 [G68] [HS66] J. E. , 1966. M. Wonham, Decentralized control and coordination of discrete-event systems with partial observation, IEEE Trans.

Definition 7. A supervisory automaton S 6 S, is said to be nonblocking relative to a language K if for every reachable state x of the closed loop automaton P × S via a string • t s ~ Le×s there exists a string t such that st c Le×s fq K and x -~P/S. -. an~'n t with ai E ]~o, ~i c •uo such thatx --+c Y where y ~ Fc (Xo, to) := (x, r) ~ (x~, r~) -% (x2, r2)... -% (x~, r',) in Bi and ev(~'i) MI'i = £~ for each i. Call the resulting automaton Bi+l. If Bi+l = Bi stop and set N = Bi ; else set i := i + 1 and go to Step 2.

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11th International Conference on Analysis and Optimization of Systems: Discrete Event Systems : Sophia-Antipolis, June 15-16-17, 1994 by Guy Cohen, Jean-Pierre Quadrat

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