GATE practice question

Question

L = {a^i b^j c^k| i=j=k or i > 1000 } is regular or not.?

Answer 1

L = {aⁱ b^j c^k | i = j = k or i > 1000}

Lets divide this into 2 languages

L₁ = {aⁱ b^j c^k | i = j = k} and L₂ = {aⁱ b^j c^k | i > 1000}

Now clearly L₁ is CSL and L₂ is regular.

$\therefore$ L = L₁ $\cup$ L₂ , which will again be a CSL.

Comments

I think it's NOT regular,as it is infinite (i,j,k are greater than 1000) no boundation on values of I,k,j .... so I think it's NOT REGULAR

m I correct?