Hardware Reference
In-Depth Information
V
M
D
Z
I
M
F
Y
M
E
V
Fig. 12.5
Instance of topology in Fig.
12.4
restricted to three FSMs
a
b
i
1
/v
1
i
2
/v
2
v
1
/
0
v
2
/
0
f
0
f
1
d
0
d
1
i
2
/v
1
v
1
/
1
i
1
/v
2
v
2
/
0
d
c
i
1
/v
1
,v
2
i
2
/v
1
,v
2
v
1
/
1
v
2
/
1
s
0
s
1
e
0
e
1
i
1
/v
2
v
2
/
1
i
2
/v
1
v
1
/
0
e
s
0
i
1
/v
2
i
2
/v
1
Fig. 12.6
FSMs with reference to the topology in Fig.
12.5
.(
a
)FSM
M
F
;(
b
)FSM
M
D
;(
c
)FSM
M
E
;(
d
) Largest solution of the system of FSM equations
M
X
M
D
Š M
F
M
D
;M
X
M
E
Š
M
F
M
E
;(
e
) Reduction with a single state of the largest solution
The largest solutions of the separate equations
M
X
M
D
Š M
F
M
D
and
M
X
M
E
Š M
F
M
E
, where the composed FSMs
M
F
M
D
and
M
F
M
E
are
specified over the input alphabet
I
and - respectively - the output alphabets
V Z
and
M
F
cannot be minimized when solving a
local FSM equation. The reason is that the output
V Y
, are equivalent to
M
F
, i.e.,
V
of the FSM
M
F
is an external
output alphabet, and so, for each component FSM
M
K
such that
M
K
M
D
M
E
is
equivalent to
M
F
M
D
M
E
, the output response of
M
K
to each input sequence
coincides with that of the FSM
M
F
, i.e., FSMs
M
F
and
M
K
are equivalent.
M
F
can be replaced with a smaller FSM when solving a
corresponding system of FSM equations, i.e., when the output
However, the FSM
V
of the FSM
M
F
is
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