This document provides an overview of Turing machines including: - Turing machines are mathematical models that can perform any computation like a computer and have an infinite tape with a tape head. - A Turing machine is defined by 7 tuples including states, alphabets, transition function, and blank symbols. - Multitape Turing machines have multiple tapes that can be accessed independently by separate heads. - The instantaneous description specifies the current state, tape symbol under the head, and full tape configuration. - Transition diagrams visually represent the transition function that specifies how the tape and state change based on the current symbol.

1. PRESENTATION
On
Turing Machine

2. Overview
 Definition of Turing Machine
 Tuples of Turing Machine
 Example of Turing Machine
 Multitape Turing Machine
 Instantaneous description for Turing Machine
 Transition diagram for Turing Machine
 Examples

3. What is Turing Machine?
 Mathematical model & more powerful than FSA & PDA.
 Do everything like a pc.
 An infinite tape.
 Has a tape head.
Tape Head

4. Tuples of Turing Machine
Turing machine has 7 tuples.
They are:
M = (Q, Σ, Γ, δ, qₒ, B, F)
 Q (finite set of states),
 ∑ (input alphabet),
 Γ (tape symbol),
 δ (transition function),
 qₒ (initial state),
 B (blank),
 F (the set of final states)

5. Example
A B C
Accept
X Y Y X B .. ..
1 Y,R
B B,R
L = 0110

6. Multitape Turing Machine (continuous)
 Ordinary Turing machine with several tapes where each tape accessed with a
separate head.
 Each head can move independently.
 Has an equivalent single tape Turing Machine.
 For N tape TM
M = (Q, Σ, Γ, δ, qₒ, B, F)

7. Multitape Turing Machine

8. Instantaneous Description
of
A Turing Machine
 Instantaneous Description or ID
X₁X₂.......Xₘ₋₁ q XₘXₘ₊₁......Xₘ
Means
- q is the current state
- Tape head is pointing to Xₘ
- X₁X₂.......Xₘ₋₁XₘXₘ₊₁......Xₘ are the current tape symbols
 δ(q, Xₘ) = (p, Y, R) is same as:
X₁X₂.......Xₘ₋₁ q XₘXₘ₊₁......Xₘ ⃓‐‐‐‐‐ X₁X₂.......Xₘ₋₁ Y p Xₘ₊₁......Xₘ
 δ(q, Xₘ) = (p, Y, L) is same as:
X₁X₂.......Xₘ₋₁ q XₘXₘ₊₁......Xₘ ⃓‐‐‐‐‐ X₁X₂.......p Xₘ₋₁ Y Xₘ₊₁......Xₘ

9. Transition Diagram for
Turing Machine (continuous)
Example:
The TM we construct will accept the language {0ⁿ1ⁿ | n>= 1}
The formal specification of TM M is,
Solution:
The transition diagram table will be

10. Transition Diagram for
Turing Machine

11. Transition Diagram for
Turing Machine
Now, the transition diagram will be,
Fig: A transition diagram for TM that
accepts the string {0ⁿ1ⁿ | n>= 1}