Automata FiniteAutomata

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Automata Theory

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Dr. Nadeem Akhtar

Assistant Professor

Department of Computer Science & IT

The Islamia University of Bahawalpur

PhD a!oratory I"ISA#UBS University of South Brittany

$uropean University of Brittany% Bretane # 'rancehttp())www*univ#u!s*fr


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Automata Theory

Automata theory is the stu+y of a!stract

computin +evices% or ,machines-*

ompu a ona mo e ea .e compu erA manageable mathematical theory can be set

up directly on a Computational model.

The simplest computational mo+el is calle+ thefinite state machine or finite automaton*

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Automata Theory

In 1234s A* Turin stu+ie+ an a!stract

machine that ha+ all the capa!ilities of

to+ay4s computers* Turin oal was to

what a computing machine could do and

what it could not do5 his conclusions apply

not only to his a!stract Turing machines% !utto to+ay4s real machines*

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Automata Theory

In the 1634s an+ 1734s% simpler 8in+s of

machines% which we to+ay call ,finite

automata- were stu+ie+ !y a num!er of

*

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Automata Theory

In the late 1734s% 9* Choms8y !ean the

stu+y of formal ,grammars- These

rammars have close relationships to

!asis of some important software

components% inclu+in parts of compilers*

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Automata Theory

In 1:% S* Coo8 e;ten+e+ Turin4s stu+y of

what coul+ an+ what coul+ not !e compute+*

Coo8 was a!leto separate those problems that

those problems that can in principle be solved,

but in practice take so much time that

computers are useless for all but very small

instances of the problem* These class of

pro!lems is calle+ ,intractable- o r ,NP-hard-*

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Automata Theory

It is hihly unli8ely that the e;ponential

improvement in computin spee+ that

computer har+ware has !een followin

impact on our ability to solve large

instances of intractable problems*

e! paes%

% % *

6# Software for verifyin systems of all types that have finite number of

distinct states% such as communications protocols or protocols for secure

e;chane of information*


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ormal definition of a inite Automaton

Afinite automaton is a 5-tuple (Q, , , qo, F)

where

1. Q is a finite set called thestates,

. s a n te set ca e t e p a et,3. : Qx Q is thetransition function,

4. qo Q is thestart state, and

5. F Q is theset of accept states.

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The finite automaton ?1 @1)0/

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The finite automaton ?1 @0)0/

A w|w contains at least one 1 and

an even number of 0s follow the last 1*

Then !("%# $ A% oreuivalently% "% recognizes A*

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The finite automaton ?0

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