$4$ Problem Set $4$

L$\_(2,3)$sub$\{0,1\}^(*)$ be the language consisting of all bit strings with at least

$2$ zeros and at least $3$ ones. Prove that this language L$\_(2,3)$T$\_($L$\_(2,3))$ Lsub$\{0,1\}^(*)$ be some language. The lengths of all words in L are

known to be squares of prime numbers. Is it true that such language

L is always non$-$regular? $($hint: not hard, pay attention to the text!$).$