ToC \ Reg Expression

Question

Give a regular expression for

L = {set of all strings in which number of a's are multiples of 3}

∑={a,b,c}

Comments

((b+c)*a(b+c)*a(b+c)*a(b+c)*)*

Answer 1

L={Set of all string in which number of a's are multiple of 3 } and ∑ ={a,b,c}

L={∊,b,bb,bbb,c,c,ccc,aaa,baaa,aaab,aaabc,abaca.....}

Regular Expression=  (  (b+c) + a (b+c)^* a (b+c)^* a  )^*

Comments

vijaycs07  multiple of 3 and no of a should be divisible by 3  both are similar kind of problems.

and yes they accept  L =( ∊,b,bb,bbb,c,c,ccc ) because  0 is multiple/divisible of 3.

 

---

Thank you @Praveen Saini sir and @Leen Sharma ....

Actually when I saw this http://www.mathwarehouse.com/answered-questions/multiples/what-are-the-multiples-of-3-solved.php then I got confused ...

But now it is clear .. because here it is given... http://mathforum.org/library/drmath/view/60913.html

---

I think it should be    (b+c)* +( a (b+c)^* a (b+c)^* a  )^*

Answer 2

For this, we will get a DFA something like this

We will have 3 states a,b,c

From a to b, one a will come

From b to c, another a will come

And from c to a, we have to come back with a transition a so that number of a gives a mod 3 = 0.

Hence ,

RE = (b* a b* a b* a) *