Computation of Flexibility in Sequential Networks - The Unknown Component Problem: Theory and Applications - page 167

x

i o

M A M B

y

Fig. 10.4 A two-way communication network of FSMs

x

i

M A M B

y

( M A ￿M B ) i×x = M KN

A

x

o

M B

y

Fig. 10.5 Wang-Brayton's construction to extend Kim-Newborn's procedure

o

u

i

M A M B

v

Fig. 10.6 Topology for latch splitting

It was shown that the input don't care sequences (those sequences which can
never occur) can be captured by the following construction. We derive .M A
M B / #i x , the composition FSM of M A and M B with input i to M A and output x
to M B asshowninFig. 10.5 . Then the Kim-Newborn construction is applied where
M A (in Kim-Newborn's procedure) is replaced by .M A M B / #i x D M KN

A

(in

Wang-Brayton's procedure).
The argument for the correctness of this is that the composition will produce the
same sequences of x is as in Fig. 10.4 . Since the configuration is now the same as
in Sect. 10.1 , the Kim-Newborn procedure can be used. We will illustrate this on an
example and compare the incompletely specified FSM produced in this way with
the largest FSM solution produced by language solving.
We use an example which is produced by latch splitting. The latch splitting
topology is shown in Fig. 10.6 ,where M B becomes the unknown component.