The document introduces Turing machines, a fundamental concept in computer science proposed by Alan Turing in 1936, which model the computing capability of a computer. It contrasts Turing machines with finite automata and pushdown automata, highlighting differences in their capabilities to accept various types of languages. A formal definition of Turing machines is provided, including their structure and operational characteristics.

1. Welcome!!
Siraj Munir – CS@DSU

2. Introduction To Turing Machine
Siraj Munir – CS@DSU

3. Tip of The Day
discourager.ignore();
(Courtesy: Syed Hammad Ahmed – CS@DSU)

4. Background
Siraj Munir – CS@DSU

5. Background
• Finite Automata accepts regular languages only.
For example: {anbn : n = 0, 1, …} is not regular, but
it is context free language.
• Pushdown Automata accepts context-free languages only.
For example: {anbncn : w  *} is not context-free.
What to do?? 
Siraj Munir – CS@DSU

6. Turing Machines

7. About:
• Introduced by Alan Turing in 1936.
• A simple mathematical model of a computer.
• Models the computing capability of a computer.
Siraj Munir – CS@DSU

8. Siraj Munir – CS@DSU
a1 a2 ….
Control
head
Tape
Informal Description
The head:
•Reads the symbol from the cell it is pointing to,
•Either:
•Writes a new symbol in the cell, or
•Moves one cell to the left or right.

9. Siraj Munir – CS@DSU
Informal Description (II)
• New cells can be added to the right of the tape as needed (similar to
RAM memory)
• These new cells contain the blank symbol, ♢
1q 2q
Rba ,
............    ca
Time 1
1q
current state


10. Siraj Munir – CS@DSU
• Transitions can be described by (Case I):
((s,a),(q;b;R)) If the machine is in state s and the current cell has an a
then jump to state q and write b in the current cell and
moves head to right.
Formal Description
• Transitions can be described by (Case II):
((s,a),(q;b;L)) If the machine is in state s and the current cell has an a
then jump to state q and write b in the current cell and
moves head to left.

11. A TM can be formally described as a 7-tuple
(Q, X, ∑, δ, q0, ♢, F) where,
Q is a finite set of states
X is the tape alphabet
∑ is the input alphabet
δ is a transition function; δ : Q × X → Q × X ×
{Left_shift, Right_shift}.
q0 is the initial state
♢ is the blank symbol
F is the set of final states
Formal Definition

12. Siraj Munir – CS@DSU
Comparison with Previous Models

13. Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata
Turing Machine
Siraj Munir – CS@DSU

14. Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata Stack (LIFO) No
Turing Machine
Siraj Munir – CS@DSU

15. Machine Data Structure Deterministic?
Finite Automata N.A Yes
Pushdown Automata Stack (LIFO) No
Turing Machine Infinite Tape Yes
Siraj Munir – CS@DSU

16. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an

17. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn

18. Siraj Munir – CS@DSU
Comparison with Previous Models
Device Type of Grammar String/Language
Finite Automata Regular an
Push Down Automata Context Free anbn
Turing Machine Unrestricted anbncn

19. Siraj Munir – CS@DSU
Questions??

20. Siraj Munir – CS@DSU
Reference:
http://www.slideshare.net/abhishiv77/push-down-automata-
vs-turing-machine
http://www.slideshare.net/AyAnKhAn5/turing-machine-
34338253
http://www.slideshare.net/dkalita3/turing-machine-bydeep
http://www.slideshare.net/lavishka_anuj/turing-machines-
12176328
https://en.wikipedia.org/wiki/Turing_machine

21. Siraj Munir – CS@DSU
Thankyou!