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Turing Machines
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Finite Automata - Turing, Study notes of Theory of Automata
In this document topics covered which are Turing Machines, The Language Hierarchy, Languages accepted by Turing Machines, Regular Language Definition, The Tape, The Input String.
Typology: Study notes
2010/2011
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Turing Machines
The Language Hierarchy
a *
Regular Languages
Context-Free Languages
n n
a b
R
ww
n n n
a b c
ww
a *b *
A Turing Machine
...... ......
Tape
Read-Write head
Control Unit
The Tape
...... ......
Read-Write head
No boundaries -- infinite length
The head moves Left or Right
...... ......
Example:
Time 0
...... ......
Time 1
- Reads
- Writes
a (^) b a c
a (^) b (^) k c
a
k
- Moves Left
...... ......
Time 1
a (^) b (^) k c
...... ......
Time 2
a f k c
- Reads
- Writes
b
f
- Moves Right
...... ......
Blank symbo
head
a (^) b a c
Input string
Remark: the input string is never empty
States & Transitions
1
q 2
q
a b,L
Read
Write Move Left
1
q 2
q
a b,R
Move Right
...... ...... a^ b a c
Time 1
1
q 2
q
a b,R
...... ...... a^ b (^) b c
Time 2
1
q
2
q
...... ...... a^ b a c
Time 1
1
q 2
q
a b,L
...... ...... a^ b (^) b c
Time 2
1
q
2
q
Example:
Determinism
1
q
2
a b,R q
Allowed Not^ Allowed
3
q b d,L
1
q
2
a b,R q
3
q a d,L
No epsilon transitions allowed
Turing Machines are deterministic
Partial Transition Function
1
q
2
a b,R q
3
q b d,L
...... ...... a^ b a c
1
q
Example:
No transition
for input symbolc
Allowed:
Example:
...... ...... a^ b a c
1
q
1
q
2
a b,R q
3
q b d,L
No possible transition
HALT!!!
Final States
1
q 2
q (^) Allowed
1
q 2
q (^) Not Allowed
- (^) Final states have no outgoing transitions
- (^) In a final state the machine halts