Communication Systems [solutions manual] by S. Haykin

By S. Haykin

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G. replace BCDE by X); step 3: define a suitable relabelling, consistent with the connection table. (With "suitable" we mean that we can use simple names -like a, b, c, ... - as the result of the relabelling. Since this relabelling is only defined within a specific context, we could use the same names in other contexts). Then apply the relabelling; step 4: apply the expansion law; step 5: reduce the resulting expressions using the ees laws. 6. Verifying large expressions ( a) substitution, (b) a CCS law.

Then the second inference rule for fairness in the case of twofold mutual recursion is: Fair-2 A = B + 7 : A + C, B = A + 7 : B + D, []AB X = 7: (C + D), [X/A,XjB]AB In other words: we replace the behaviour equations for A and B by the behaviour equation for X. At the same time, within the behaviour equations in which A and B occur, we replace the agent identifiers A and B by the agent identifier X. 2. FIFO communication 53 before applying rule (Fair-2) after applying rule (Fair-2) A=B+r:A+C B=A+r:B+D C = ..

8 6 S4 = xl? : 86 S5 = dO! : 8 2 S6 = dl! :R2 We assume that the occurrence of a timeout is caused by the loss of an acknowledgement. This allows us to model the timeout within the channel. e. as soon as one of the actions dO? or d1? occurs. The event where the timer expires will be modeled as an action timeout!. 1. e. aO, aI, etc. • The calculation yields (with renaming of the agent identifiers): (1) (3) (6) S1 S2 83 (10) 84 (11) S5 (14) S6 (16) S7 = xO? : S2 = T : yO! : 83 + T : 8 2 = T : xl?

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