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1. DEPARTMENT OF COMPUTRSCIENCE AND APPLICATION
ATALBIHARI VAJPAYEEUNIVERSITYBILASPUR(C.G.)
Topic :- Turing Machine: Formal Definition and Behaviour, Transition Diagram,
Acceptance by Turing Machine.
PRESENTED BY :-
.Aniket Singh
.Krishna Dewangan
.Suraj sahu
.Ravindra Nishad
Class :- MSC 1st year 1st Sem
Subject :- Theory of Computation
PRESENTED To :-
Prerna Mam

2. Transition Diagram
Acceptance by Turing Machine
Turing Machine: Formal Definetion and Behaviour

3. Turing
Machine:--
A L A N T U R I N G
2 3 J u n e 1 9 1 2
To
0 7 J u n e 1 9 5 7

4. INTRODUCATION TO TURING MACHINE:--
• Invented by esteemed Computer Scientist ALAN TURING IN 1936.
• Basically an abstract computational model that perform
computations.
• Provide a powerful computational model for solving problems in
computer science
• Capable of simulating common computers.
• It has unlimited memory capability.

5. Turing machine was invented in 1936 by Alan Turing. It is an accepting device which
accepts Recursive Enumerable Language generated by type 0 grammar
Turing machine can accept all this language
T.M Recursively Enumerable LanguageT.M
P.D.A Context Free LanguageP.D.A
F.A Ragular LanguageF.A
EX.  an bn PDA
an bn cn TM

6. Q  Set of finite states
∑ finite set of I/P Alphabet not containing B READ/WRITE HEAD
Γ  finite set of tape symbol including (∑≤ Γ )
B  Special symbol represtnting Blank cell (B )
q0 is initial state (q0 )
F Set of final state (F ≤ Q)
δ A transition or mapping function.
Q × Γ  Q × Γ × ( L,R )
(q0, a) (q1 × X , R/L )
M=[ Q, ∑, Γ, B, q0, F, δ ] {7 tuple}
Formal definition of Turing machine
… B B a b a B B B …
Finite control

7. Turing Machine has infinite size tape and it is used to accepted Recursively Enumerable
Language
L R
TM Read also allow as well as wright is also allow
TM can move in both directions [left/right]
TM is a mathematical model which consists of an infinite length tape divided into cells
which I/P is give if consist of a head which reads the I/P tape
After reading an I/P symbol , it is replaced with another symbol it is replaced with another
symbols it internal state is change it moves from one cell to the right n left
A B
q1 q0 q0 (state)
a b b

8. If the TM reaches the final state I/P string accepted
otherwise rejected
The RULE :--
1. You can read cell by cell
2. You can change the content to the cell
3. You can move to the right or to the left
Cannot do this :--
1. You cannot jump from a cell to a far cell just cell next to each
other
2. We will give you set of thing you can use them only as input to our
machine
B B a b b

9. B B X a a Y b b B B
 Let us understand the approach by taking the example
“aaabbb”.
Scan the input from the left.
First, replace an ‘a’ with ‘X’ and move right. Then skip all the a’s and b’s and move right.
When the pointer reaches Blank(B) Blank will remain Blank(B) and the pointer turns left.
Now it scans the input from the right and replaces the first ‘b’ with ‘Y’. Our Turing
machine looks like this –

10. Again the pointer reaches Blank(B) or X. It now scans the input from left to right. The pointer moves
forward and replaces ‘a’ with ‘X’.
Again the pointer reaches Blank(B) or Y. It now scans the input from the right to left. The pointer moves
forward and replaces ‘b’ with ‘y’.
We repeat the same steps until we convert all the a’s to ‘X’ and b’s to ‘Y’. When all the a’s converted to ‘X
and all the b’s converted to ‘Y’ our machine will halt.

11. accepted by Turing machine
The turing machine accepts all the language even though they are recursively enumerable.
Recursive means repeating the same set of rules for any number of times and enumerable
means a list of elements. The TM also accepts the computable functions, such as addition,
multiplication, subtraction, division, power function, and many more.
Example: Construct a turing machine which accepts the language of aba over ∑ = {a, b}.
Solution:
We will assume that on input tape the string 'aba' is placed like this:
The tape head will read out the sequence up to the Δ characters. If the tape head is readout
'aba' string then TM will halt after reading Δ.

12. Now, we will see how this turing machine will work for aba. Initially, state is q0 and
head points to a as:
The move will be δ(q0, a) = δ(q1, A, R) which means it will go to state q1, replaced a by A and
head will move to right as:

13. The move will be δ(q1, b) = δ(q2, B, R) which means it will go to state q2,
replaced b by B and head will move to right as:
The move will be δ(q2, a) = δ(q3, A, R) which means it will go to state q3, replaced a by A and
head will move to right as:
The move δ(q3, Δ) = (q4, Δ, S) which means it will go to state q4 which is the HALT state and HALT state
is always an accept state for any TM.

14. The same TM can be represented by Transition Table:
States a b Δ
q0 (q1, A, R) – –
q1 – (q2, B, R) –
q2 (q3, A, R) – –
q3 – – (q4, Δ, S)
q4 – – –

15. The same TM can be represented by Transition
Diagram: