2,298 views
1 votes
1 votes

The regular expression corresponding to the finite automata given below is

  1. (ab*(a+b)+ϵ)*
  2.   (ϵ+a(a+b)b*a)*
  3.   ((ϵ+(a+b)ab*)a)*
  4.   (ab*(a+b)a+a)*(ab*(a+b)+ε)

1 Answer

Best answer
4 votes
4 votes
write the state equations

$A= \epsilon + Ba$

$B= A\epsilon + C(a+b)$

$C= Aa + Cb$

Apply Arden's Theorem $[\text{if}\; R= Q+RP\; \text{then} \;R = QP*]$

$C= Aab^*$

put equation of $C$ in $B$

$B= A(\epsilon +ab^*(a+b))$

put equation of $B$ in $A$

$A=\epsilon+ A(\epsilon +ab^*(a+b))a$

Apply Arden's Theorem

$A=((\epsilon +ab^*(a+b))a)^*$

put equation of $A$ in $B$

so  $B=((\epsilon +ab^*(a+b))a)^*(\epsilon+ab^*(a+b))$
selected by

Related questions

3 votes
3 votes
1 answer
1
Deepak Sharma 1 asked Aug 17, 2015
862 views
Let A= (a + b)* ab (a + b)*,B= a*b* andC= (a + b)*.Then the relation between A, B and C:A. A+B= C B. A+Reverse(B)= C C. Reverse(A)+B= C D. None
0 votes
0 votes
1 answer
3
dutta18 asked Sep 21, 2022
415 views
What is the Finite Automata( NFA, epsilon-NFA or DFA) for the regular expression (a*ba)* ?
2 votes
2 votes
2 answers
4