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+16 votes

The regular expression for the language recognized by the finite state automaton of figure is ______

asked in Theory of Computation by Veteran (59.5k points) | 1.2k views
0* 1 1* 0 (0+1)* this is the language in which every 1 is must followed by 0

@Bikram sir my doubt is how to complement this ?
0* 1 1* 0 (0+1)* why this is wrong
i also make the sm mistake :P

3 Answers

+26 votes
Best answer

$L$ contains all binary strings where a $1$ is not followed by a $0$.
answered by Boss (40.2k points)
edited by
It can also be 0*11*+0*
@gatemate  u right R.E for each final state and apply in b/w '+' mans OR then u got 0*+0*11* then take common 0*(epsilion+11*) ans as we know (epsilon+rr*)=r*  so here we get 0*1*
Yes, I am also getting this answer.
0 votes
A grammer not containing 10 as substring
answered by Active (1.9k points)
0 votes

Clearly , looking into DFA we can say that C is Dead state.

Using Arden's theoram to find the regular expression :

A = ε + A0ε0* = 0*

B = A1 + B1 = 0*1 +B1 = 0*11* = 0*1*

Therefore answer is 0*1*

PS : Ardens theoram - 

Let P and Q be two regular expressions.

If P does not contain null string, then R = Q + RP has a unique solution that is R = QP*

answered by Active (1.4k points)

How did you simplified B = A1 + B1 = 0*1 +B1 = 0*11*.

according to Arden's theorem shouldn't it be: B=B.1+0*11* =1*0*1 ?


B= 0*1 + B1

R=B, Q=0*1 and P=1

then by arden's theorem,




u have to union both the A and B values becoz there are two final states n given FA

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