TOC Identify Language

Question

Check for Regular,CFL,CSL?

1. L={a^n b^m | LCM(n,m)=600) }

2.L={a^n b^m | LCM(n,m)=k) }

3. L={a^n b^m | GCD(n,m)=600) }

4.L={a^n b^m | GCD(n,m)=k) }
 

I think first is CFL as we will have limited cases where LCM is 600 but for second one it should be CSL.

For GCD whether it is constant 600 or k,we will have infinite cases.So it must be CSL.

Please verify answer and approach

Comments

For Your question.Yes.{e,2,3.....}* .I can generate everything from 2 and 3,so regular.

 I got my doubt actually:) that p variable is not consumed by any input which is making it regular.If there was some c,that is consuming p/k that some will become not regular..I will create a similar new question where p will be consumed by some variable.This question is clear.Thanks:)

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Added:- https://gateoverflow.in/142081/toc-identify-language .Please check it once.

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@joshi_nitish can u please explain these in details.

Answer 1

can someone explain these all four options i am not getting it