Finite-State Machines
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Transcript of Finite-State Machines
Finite-State Machines
2
Transition assigned machine (Mealy)
1/1
B
D
CA
0/00/1 0/1
0/01/1
1/0 1/0
3
State assigned machine (Moore)
B, 1
D, 3
C, 2A, 0
1
1
1
1
0 0
00
D B 0
A C 1
B D 2
C A 3
A
B
C
D
0 1
(a) State Diagram (b) State Table
4
Construction of Ms from Mt
0/1
BA
0/01/1
1/0
Ms :Mt :0
(A, 0), 0 (B, 0), 0
(A, 1), 1 (B, 1), 1
00
1
1
1
1
0
5
Example of the partitioning procedure
A
B
C
D
0 1
E
F
G
H
J
B, 0 C, 0
C, 1 D, 1
D, 0 E, 0
C, 1 B, 1
F, 1 E, 1
G, 0 C, 0
F, 1 G, 1
J, 1 B, 0
H, 1 D, 0
M:
P1: {A, C, F}, {B, D, E, G}, {H, J}
P2: {A, F}, {C}, {B, D, E, G}, {H, J}
P3: {A, F}, {C}, {B, D}, {E, G}, {H, J}
P4: {A}, {F}, {C}, {B, D}, {E, G}, {H, J}
00
00
11
6
Construction of a reduced machine
NewNamesin M
{A}P4:
'
{F} {C} {B, D} {E, G} {H, J}
U V W X Y Z
(a)
(b)
{B}, 0 {C}, 0
{G}, 0 {C}, 0
{D}, 0 {E}, 0
{C}, 1 {D, B}, 1
{F}, 1 {E, C}, 1
{J, H}, 1 {B, D}, 0
U {A}
V {F}
W {C}
X {B, D}
Y {E, G}
Z {H, J}
0 1New
Names Blocks
7
Testing two machines for equivalence
A
B
C
0 1
B, 0 A, 0
A, 0 C, 1
C, 1 A, 0
0 1
D
E
F
G
H
E, 0 D, 0
D, 0 F, 1
F, 1 D, 0
E, 0 H, 1
D, 1 G, 0D
E
F
G
H
E, 0 D, 0
D, 0 F, 1
F, 1 D, 0
E, 0 H, 1
D, 1 G, 0
A
B
C
0 1
B, 0 A, 0
A, 0 C, 1
C, 1 A, 0
M1
M2
(a) M1 (b) M2 (c) Sum of M1 and M2
P1 : {A, D}, {B, E, G}, {C, F, H}
P2 : {A, D}, {B, E}, {G}, {C, F}, {H}
P3 = P2