Complete Language


Given the language L={ab, aa, baa}, which of the following strings are L*?

  1. abaabaaabaa
  2. aaaabaaaa
  3. baaaaabaaaab
  4. baaaaabaa


all except the 3rd one.


The correct options are:1,2,4

Explanation :

L = { ab, aa, baa }
Let S1 = ab , S2 = aa and S3 =baa
abaabaaabaa can be written as S1S2S3S1S2
aaaabaaaa can be written as S1S1S3S1
baaaaabaa can be written as S3S2S1S2


here * means klean closure operator.
a* means zero or more instances of a i.e. {ephselon,a,aa,aaa,…}
so given language is L={ab,aa,baa}
let A=ab B=aa C=baa
in third option(CBABBb) here b is this string doesn’t belongs to L so option 3 is incorrect
consider remaining options all are correct