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a
1/1
b
1/1
0/0
0/0
0/0
0/1
2
2
1
1
0/0
0/0
1/0
1/0
1/1
1/1
3
3
c
1/1
0/0
0/1
22
11
0/0
−/−
1/1
33
3T
1/−
M
B
Fig. 5.2
Components (
a
) M
A
and (
b
) M
B
of series topology M
A
!
M
B
of Example
5.1
;(
c
)
M
B
can be reduced to two
expresses the full flexibility at M
B
due to input don't care sequences;
states by state minimization
5.1.3
Computation of Output Don't Care Sequences
Output observability don't cares are the sets of sequences of inputs of M
B
that
cannot be distinguished by the outputs of M
B
, i.e., the sequences of a set cannot
be distinguished from each other by looking to the outputs of M
B
; they restrict the
observability of the driving FSM M
A
and are used to modify M
A
obtaining an FSM
M
A
such that the cascade interconnection does not change, i.e.,
M
A
!
M
B
D
M
A
!
M
B
.
5.1.3.1
Computation of Subsets of Output Don't Care Sequences
Output don't cares sequences of length one (called simply sequential output don't
cares), were studied by Devadas [34], and fixed-length output don't care sequences
by Rho [121].
A different subset of output don't care sequences of M
A
is computed by a
procedure designed by Wang [140], whose idea is to enumerate implicitly all
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