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# Introduction to Turing Machine

1. Introduced by Alan Turing in 1936.
2. A simple mathematical model of a computer.
3. Models the computing capability of a computer.

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### Introduction to Turing Machine

1. 1. Welcome!! Siraj Munir – CS@DSU
2. 2. Introduction To Turing Machine Siraj Munir – CS@DSU
3. 3. Tip of The Day discourager.ignore(); (Courtesy: Syed Hammad Ahmed – CS@DSU)
4. 4. Background Siraj Munir – CS@DSU
5. 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. 6. Turing Machines
7. 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. 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. 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. 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. 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. 12. Siraj Munir – CS@DSU Comparison with Previous Models
13. 13. Machine Data Structure Deterministic? Finite Automata N.A Yes Pushdown Automata Turing Machine Siraj Munir – CS@DSU
14. 14. Machine Data Structure Deterministic? Finite Automata N.A Yes Pushdown Automata Stack (LIFO) No Turing Machine Siraj Munir – CS@DSU
15. 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. 16. Siraj Munir – CS@DSU Comparison with Previous Models Device Type of Grammar String/Language Finite Automata Regular an
17. 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. 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. 19. Siraj Munir – CS@DSU Questions??
20. 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. 21. Siraj Munir – CS@DSU Thankyou!

1. Introduced by Alan Turing in 1936. 2. A simple mathematical model of a computer. 3. Models the computing capability of a computer.

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