Let r, s, and t be regular expressions over ∑ = { a ,   b } . In 28—30, determine whether the two regular expressions define the same language. If they do, describe the language. If they do not, give an example of a string that is in one of the languages but not the other.

29. ( r s ) * and r * s *

Determine whether the two regular expressions define the same language. If they do,

describe the language. If they do not, give an example of a string that is in one of the

languages but not the other.

(rs)* and r*s*

Given information:

r,s,t be the regular expression.

Concept used:

Here (a,b)* represents any string at all made up of a's and b's, this part is followed by ab which is followed by any one of the expression aa,ab,ba or bb.

Calculation:

The alphabet ∑={a,b,c} is defined over the regular expressions r,s and t.

Two regular expressions r and s are equivalent if L(r)=L(s).

Use the following definitions:

Recursion: L(rr')=L(r)L(r')  and L(r*)=(L(r))*

Now check whether L(( rs)*)=L(r*s*) as follows:

L( ( rs )*)=(L( rs))*=(L( r)L( s)