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In-Depth Information
a
i
2
v
1
z
1
/o
1
i
2
v
1
z
2
/o
2
s
0
s
1
i
1
v
1
z
1
/o
1
i
1
v
1
z
2
/o
2
i
1
v
2
z
1
/o
1
i
1
v
2
z
2
/o
2
i
2
v
1
z
1
/o
1
i
2
v
1
z
2
/o
2
i
1
v
1
z
1
/−
i
1
v
1
z
2
/−
i
2
v
2
z
1
/−
i
1
v
2
z
1
/−
i
1
v
2
z
2
/−
i
2
v
2
z
1
/−
i
2
v
2
z
2
/−
i
2
v
2
z
2
/−
s
2
−−−/−
b
c
i
2
v
1
z
1
/o
1
i
2
v
1
z
2
/o
2
v
1
z
1
/o
1
v
1
z
2
/o
2
s
0
s
1
s
0
s
1
i
1
v
1
z
1
/−o
1
i
1
v
1
z
2
/−o
2
i
1
v
2
z
1
/−
i
1
v
2
z
2
/−
i
2
v
2
z
1
/−
i
2
v
2
z
2
/−
v
1
z
1
/o
1
v
1
z
2
/o
2
i
1
v
2
z
1
/o
1
i
1
v
2
z
2
/o
2
i
2
v
1
z
1
/o
1
i
2
v
1
z
2
/o
2
v
2
z
1
/o
1
v
2
z
2
/o
2
v
1
z
1
/o
1
v
1
z
2
/o
2
i
1
v
1
z
1
/o
1
v
1
z
1
/o
1
v
1
z
2
/o
2
v
2
z
1
/o
1
v
2
z
2
/o
2
i
1
v
1
z
2
/o
2
i
2
v
2
z
1
/o
1
v
2
z
1
/−
v
2
z
2
/−
i
2
v
2
z
2
/o
2
s
2
s
2
−−−/−
−−/−
d
v
1
z
1
/o
1
v
1
z
2
/o
2
v
1
z
1
/o
1
v
1
z
2
/o
2
v
1
z
1
/o
1
v
1
z
2
/o
2
v
1
z
1
/o
1
v
2
z
1
/o
1
v
1
z
2
/o
2
v
2
z
2
/o
2
s
0
s
0
s
1
s
0
s
1
s
2
s
0
s
1
v
2
z
1
/o
1
v
2
z
2
/o
2
v
2
z
1
/o
2
v
2
z
2
/o
1
v
2
z
1
/−
v
2
z
2
/−
v
1
z
1
/o
2
v
1
z
2
/o
1
v
2
z
1
/−
v
2
z
2
/−
v
1
z
1
/o
2
v
1
z
2
/o
1
v
2
z
1
/o
2
v
2
z
2
/o
1
s
2
v
1
z
1
/−
v
1
z
2
/−
v
2
z
1
/−
v
2
z
2
/−
Fig. 14.5
(
a
) Largest solution M
S
for FSM equation from Example
14.6
;(
b
) Permissible
transitions w.r.t. input alphabet I of largest solution M
S
;(
c
) .M
S
/
#
V
Z
O
, i.e., M
S
restricted
to input alphabets V
Z and output alphabet O;(
d
)
M
S
.M
S
/
d
D
#
V
Z
O
, determinization of
.M
S
/
#
V
Z
O
M
S
.M
S
/
d
We then check whether
D
#
V
Z
O
depends essentially on the input
M
S
.M
S
/
d
alphabet V . FSM
#
V
Z
O
has no V -forbidden states; we just delete
the transitions that are not permissible, namely, the transitions
v
2
z
1
=o
2
and
v
2
z
2
=o
1
D
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