By J.P. Perrin, M. Denouette, E. Daclin
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Extra info for Switching Machines: Volume 2 Sequential Systems
Azerb. S. S. R 3 (1965) 20-29. Sc. thesis in aeronautics by F. Saez Vacas which was completed under the authors' direction and deals with the use of a computer in the abstract synthesis of asynchronous machines using Gloushkov's method. 46 SWITCHING MACHINES asynchronous and synchronous systems is that of the existence of stable states in the asynchronous systems. How can this be shown in the representation of asynchronous controls by regular expressions? We have seen (chapter introducing sequential systems) that the duration of a control in synchronous systems should be very small with respect to the circuit's response time A if the circuit is to be selfevolving.
Note that A==B==C==D E==G F==H J==K L==M. From simple inspection of the table, we see that the last two identities noted above imply: J == K == L == M. LetA = 1, E = 2, F = 3,J = 4. 36(a) table in which the stable states have been circled. Nevertheless, this table is not the simplest. 35(a). 35(b). G (X2 , 2) and G (X2 , 3) cannot figure in the table since from the configuration of the internal states 2 and 3, it is impossible to receive X 2 (that is, B) at this moment. These two next states can therefore be replaced with 'don't cares'.
41 SYNTHESIS OF THE TABLES We begin by the indexation of the places. The primitive places are indexed as follows: R(Z) = I(XII+~21+~31)~1~2~31· 0123456 The rules of index extension lead to the following: o 1 2 3 o o 1 2 3 0 1 1 2 3 2 3 In order to obtain the Moore table of the sequential machine which realizes this regular expre~sion, we must study the problem in more detail. 30). Note also that among these 27 sequences, 9 begin with Xl' 9 with X 2 , and 9 with X 3 • It is also to be noted that 3 sequences begin withX I X 2 , and 3 end withX2X 3 • We note that only one sequence interests us: X I X 2X 3 (which we shall call the 'good sequence' or 'interesting sequence').