made easy theory of computation regular expression

Question

which one of the following regular expression describe the language over {a,b} consist of no pair of consecutive a’s?

a.    (b*abb*) (a+€)

b.    (b+ab)* (a+€)

c.     (b*abb*)*(a+€)+b*

d.    (b*ab*)*(a+€)+b*(a+€)

Comments

option B is correct.

Answer 1

(b) is Correct.

(a) fails for L= {abab, ababa,..}, given regular expression doesn't represents {abab, ababa,..}. Observe this option is not capable of representing more than 2 a's in an expression. therefore abababa... and for all such expressions it will fail

(c) fails for L= {ba}, given regular expression doesn't represents {ba} which canbe easily observed

(d) fails because it represents aa,aaa,aaaa.., which it should not.

Comments

Thank you

How A doesn't represent {a}

C doesn't represent {ba} explain