in Theory of Computation
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if concatenation of two languages $L_1\ and\ L_2(L_1.L_2)$  is regular then what can we say about $L_1\ and\ L_2 $ ??

is there any possibility of  $L_1=nonregular\ ,\ L_2=nonregular \   $ ?? 

in Theory of Computation
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4 Comments

Ok L2^nonPrime will derive eps and 0 but what if u concatenate with L1?

The smallest string in L1 is 0² so any thing concatenated with L1 would never generate less than 0².

Am i right?
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Yes, you are right. :D edited.
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@Aamabazinga good explanation bro:)
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1 Answer

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is there any possibility of  L1=nonregular , L2=nonregular  ?? 

YES!

One can come up with many example but I’ll state one of the standard and easy to understand.

Goldbach's conjecture : It states that every even natural number greater than 2 is the sum of two prime numbers.

L={1^p:p is an odd prime} If the Goldbach conjecture is true then L.L=(11)^+ is regular, but L isn't.