Identify the class of given mod based language

Question

L = {aⁿb^m | n mod m = 0 , n>=0 , m>0} Given language is

A) CFL

B) CSL

C) DCFL

D) REC

E) RE

Comments

let determine ans for m>0,,, not as m>=0, actually question culd be like a^nb^m | n is divisible by m

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To put it simply, the accepter here requires the power of a divider. For example, if there are $p$ number of a's where $p$ is a prime number then string must not be accepted if number of b's is not 1 or 'p'. We can also use pumping lemma to show it is not CFL.

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So, it should be CSL ?? nd sir, i m not good in pumping lemmas..but ya, I think it requires division so shud be CSL.

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yes. Whatever you can write a C code for, will be a CSL. Options D and E are also true. But CSL is the most appropriate.

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@arjun sir :can't we write the above language as -:

$L=\left \{ a^{n}b^{m} | n=k \times m\right \}$ there is no way to check this language using  stack.