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Recently, I was facing some problems in effectively proving the following :

Consider the alphabet Σ ={0,1,2,...,9,#}, and the language of strings of the form x#y#z, where x,y and z are strings of digit such that when viewed as numbers, satisfy the mathematical equation x+y=z.

For example, the string 123#45#168 is in this language because 123 + 45 = 168.

Is this language regular and why ?

I was trying to apply the Pumping Lemma, but am unsure of how to complete the proof. Could anyone please help ?

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  • $\begingroup$ Can you please show how far you got with your proof? Somehow, the language reminds me of $a^n y b^n$. $\endgroup$
    – greybeard
    Commented Sep 15, 2020 at 6:15

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Hint:

Consider the special case where $y=0$.

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