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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*
0
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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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The finite automaton ?0
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The finite automaton ?2
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The finite automaton ?2
1:
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The finite automaton ?6
1