introduction to turing machine

Welcome!!

Siraj Munir – CS@DSU

Introduction To Turing Machine


Tip of The Day

discourager.ignore();

(Courtesy: Syed Hammad Ahmed – CS@DSU)

Background


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??


Turing Machines

About:

• Introduced by Alan Turing in 1936.

• A simple mathematical model of a computer.

• Models the computing capability of a computer.



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.


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 2qRba ,

............ ca

Time 1

1qcurrent state


• 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.

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

Formal Definition


Comparison with Previous Models

Machine Data Structure Deterministic?

Finite Automata N.A Yes

Pushdown Automata

Turing Machine




Pushdown Automata Stack (LIFO) No

Turing Machine




Pushdown Automata Stack (LIFO) No

Turing Machine Infinite Tape Yes



Comparison with Previous ModelsDevice Type of Grammar String/Language

Finite Automata Regular an




Push Down Automata Context Free anbn




Push Down Automata Context Free anbn

Turing Machine Unrestricted anbncn


Questions??


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


Thankyou!

introduction to turing machine

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