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)
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)
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