Is this a regular set oddlength binary strings representing

Is this a regular set: {odd-length binary strings representing perfect powers of 2}? Prove your answer.

Solution

Regular Expression :

A sequence of symbols and characters expressing a string or pattern .

ex : RegE₁ = a(aa)^* and RegE₂ = (aa)^*

Regular Sets :

Any set that represents the value of the Regular Expression is called a Regular Set.

ex: L₁= {a, aaa, aaaaa,.....} (Strings of odd length excluding Null)

Now given sentance : odd length binary strings representing perfect powers of 2.

Odd length binary strings set ={000,001,010,100,101,110,111,11111,10001,.....}={0,1,2,3,4,5,6,7,31,17,...} .This set does not contain perfect squares .so the given thing does not represents regular set.