Hardware Reference
In-Depth Information
a
b
0
/
1
1
/
1
00
/
11
11
/
01
1
4
a
b
10
/
11
0
/
1
00
/
01
01
/
10
11
/
10
10
/
01
00
/
11
10
/
11
1
/
1
1
/
1
01
/
10
01
/
01
11
/
10
2
3
0
/
1
c
0
/
0
1
/
0
c
d
a
1
a
1
1
/
0
1
/
0
1
/
1
1
/
1
0
/
1
0
/
1
0
/
0
0
/
0
0
/
0
0
/
0
a
2
,b
4
a
2
,c
4
a
2
,b
4
a
2
,c
4
0
/
1
0
/
1
0
/
0
0
/
0
1
/
0
1
/
0
1
/
0
0
/
1
0
/
1
0
/
1
0
/
0
1
/
0
1
/
0
a
1
,b
3
a
1
,c
3
dc
a
1
,b
3
dc
1
/
1
−/−
−/−
1
/
1
1
/
1
1
/
0
0
/
1
1
/
1
0
/
1
1
/
1
0
/−
0
/
1
c
3
b
3
c
3
b
3
1
/
1
1
/
1
Fig. 3.8
Illustration of Example
3.26
.(
a
) FSM M
A
;(
b
) FSM M
C
;(
c
) Largest FSM solution M
X
;
(
d
) Largest Moore FSM solution
Moore
.M
X
/
Example 3.26.
Consider the equation M
A
M
X
M
C
, with M
A
and M
C
shown,
respectively, in Fig.
3.8
a,b. The largest FSM solution M
X
is shown in Fig.
3.8
c,
whereas Fig.
3.8
d shows the largest Moore FSM solution
Moore
.M
X
/. Moore
FSM solutions are portrayed in Fig.
3.9
a,b, whereas nonMoore FSM solutions are
pictured in Fig.
3.9
c,d.
3.4
Solution of FSM Equations Under Parallel Composition
3.4.1
Largest FSM Solution
Given alphabets I
1
;I
2
;U;V;O
1
;O
2
, an FSM M
A
over inputs I
1
[
V and outputs
U
[
O
1
, and an FSM M
C
over inputs I
1
[
I
2
and outputs O
1
[
O
2
, consider the
FSM equations
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