This presentation summarizes Turing machines, including: - Turing machines were introduced by Alan Turing in 1936 as a mathematical model of computation. - A Turing machine consists of a finite state control, a tape divided into cells, and a tape head that can read and write symbols on the tape and move the tape left and right. - Turing machines are formally defined by a 7-tuple that specifies the states, tape alphabet, transition function, blank symbol, start state, and accepting states.

1. Presentation
on
Turing Machine
Presented By :
Kanis Fatema
17102010
Monisha Dey
17102032
Rezuana Khatun
16102033

2. Objectives
 Definition
 Formal Definition
 Representation of Turing Machine
 Model of Turing Machine
 Transition Function
 Transition Diagram
 Instantaneous Description
 Multi-tape Turing Machine
 Example

3. INTRODUCING TURING MACHINES
 by Alan Turing in 1936.
 mathematical model of a computer.
 computing capability of a computer.

4. DEFINITION
 a finite-state machine
 a tape head that can read or write one
tape cell and move left or right.
 accepts the input string
 used for input and working storage.

5. Representation of Turing Machine
Turing Machine is represented by
M=(Q, ∑, Γ,δ,q0,B,F) ,
Where
Q is the finite state of states
∑ a set of Γ not including B, is the set of input symbols,
Γ is the finite state of allowable tape symbols,
δ is the next move function, a mapping from Q × Γ to Q × Γ
×{L,R} Q0 in
q0 is the start state,
B a symbol of Γ is the blank,
F is the set of final states.

6. THE TURING MACHINE MODEL

7. TRANSITION FUNCTION
One move (denoted by |---) in a TM does the
following:
δ(q , X) = (p ,Y ,R/L)
 q is the current state
 X is the current tape symbol pointed
by tape head
 State changes from q to p

8. Transition Diagram

9. Instantaneous Description For
Turing Machine
ID of a Turing Machine is a snapshot of Turing Machine to describe the
current situation of the Turing Machine.
 X1 X2…Xi-1 q Xi Xi+1 …Xn
Means:
• q is the current state
• Tape head is pointing to Xi
• X1X2…Xi-1XiXi+1… Xn are the current tape symbols
 δ (q , Xi ) = (p ,Y , R ) is same as:
X1 X2…Xi-1 q Xi Xi+1 …Xn |---- X1 X2…Xi-1 Y p Xi+1…Xn
 δ (q ,Xi) = (p, Y ,L) same as:
X1 X2…Xi-1 q Xi Xi+1 …Xn |---- X1 X2…pXi-1Y Xi+1 …Xn

10. MULTITAPE TURING MACHINES
 A Turing Machine with several tapes
 Every Tape have their Controlled own R/W
Head
 For N- tape TM M=(Q,∑, Γ,δ,q0,B,F)
 we define δ : Q X ΓN Q X ΓN X { L , R} N

11. A Multi-tape Turing machine can be formally described as a
6-tuple
(Q, ∑, B, δ, q0, F)
where −
Q is a finite set of states
∑ is the tape alphabet
B is the blank symbol
δ is a relation on states and symbols where
δ: Q × Xk → Q × (X × {Left_shift, Right_shift, No_shift })k
where there is k number of tapes
q0 is the initial state
F is the set of final states

13. Uses Of Turing Machine
 language recognizer
 language generator
 language evaluator
 language decider

14. Transition Diagram of Turing Machine
 The formal specification of the Turing Machine M that accept the language
{0n1n | n ≥ 1}is,
M = ({q0, q2, q3,q4},{0,1},{0,1,X,Y,B}, δ, q0, B, {q4})
where δ is given in the table below,

15. q0
q1
q3
q2
q4
0/0
1/Y
X/X
Y/Y
Y/Y
B/B
Y/Y
0/0
Y/Y
0/X

16. Question?

17. Thank You