turing machine read/write – move left/right bb read/write head 001000 state qi
TRANSCRIPT
Turing MachineRead/Write – Move Left/Right
B B
Read/Write Head
0 0 1 0 0 0
State Qi
State Diagram for Modulus 3shows only the tape input
Q0
Q1
Q2
Start 1
1
00
1
0
Q3 Q4
BB
B
B,0,1
Turing MachineProgram To Compute Values
Modulus 3State, Write, Direction
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
Modulus 353 % 3
B B1 1 0 1 0 1
State Q0
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
New State – Write B
Modulus 353 % 3
B BB 1 0 1 0 1
State Q1
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
Modulus 353 % 3
B BB B 0 1 0 1
State Q0
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
Write B
Modulus 353 % 3
B BB B B 1 0 1
State Q0
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L New State – Write B
Modulus 353 % 3
B BB B B B 0 1
State Q1
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,LNew State – Write B
Modulus 353 % 3
B BB B B B B 1
State Q2
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,LWrite B
Modulus 353 % 3
B BB B B B B B
State Q2
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
New State – Write 0
Modulus 353 % 3
B 0B B B B B B
State Q4
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
New State – Write 1
Modulus 353 % 3
B 0B B B B B 1
Q3 Halt
State B 0 1
Q0 3,0,L, 0,B,R 1,B,R
Q1 3,1,L 2,B,R 0,B,R
Q2 4,0,L 1,B,R 2,B,R
Q3 Halt Halt Halt
Q4 3,1,L 3,1,L 3,1,L
Turing MachineProgram To Add Unary Numbers
State, Write, Direction
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 3,1,Halt Halt 3,1,L
Adding Two Unary Numbers2 + 3 = 5
B B1 1 0 1 1 1
State Q0
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 0 1 1 1
State Q0
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 0 1 1 1
State Q0 New State – Write B
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 1
State Q1
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 1
State Q1
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 1
State Q1
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 1
State Q1New State
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 1
State Q2
New State – Write B
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 B
State Q3
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 B 1 1 B
State Q3
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Adding Two Unary numbers 2 + 3 = 5
B B1 1 1 1 1 B
Q3 HALT HALT – Write 1
State B 0 1
Q0 Halt 1,B,R 0,1,R
Q1 2,B,L Halt 1,1,R
Q2 Halt Halt 3,B,L
Q3 - 1,Halt Halt 3,1,L
Turing MachineProgram To Subtract Unary Numbers
State, Write, Direction
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Turing Machine with Halt State Program To Subtract Unary Numbers
State, Write, Direction
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,4 1,B,4 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,4 3,B,4 0,B,R
Q4 Halt Halt Halt
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 1
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 1
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
. . .
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 1
State Q1
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 B
State Q2
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 B
State Q2
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 B
State Q2
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
. . .
Subtracting Two Unary Numbers5 − 2 = 3
B B1 1 1 0 1 B
State Q3
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 1 B
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 1 B
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
. . .
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 1 B
State Q1
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 B B
State Q2
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 B B
State Q2
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
. . .
Subtracting Two Unary Numbers5 − 2 = 3
B BB 1 1 0 B B
State Q3
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB B 1 0 B B
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB B 1 0 B B
State Q0
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 2,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
. . .
Subtracting Two Unary Numbers5 − 2 = 3
B BB B 1 0 B B
Q1
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 1,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R
Subtracting Two Unary Numbers5 − 2 = 3
B BB B 1 B B B
Q1 Halt Write Blank
1 1
State B 0 1
Q0 1,B,L 0,0,R 0,1,R
Q1 1,B,Halt 1,B,Halt 2,B,L
Q2 3,B,R 2,0,L 1,1,L
Q3 3,B,Halt 3,B,Halt 0,B,R