Is $L = \{a^{i+j}b^{j+k}c^{i+k} | i,j,k > 0\}$ context free?

Question

This is not an assignment question. Professor gave this for us to think about. I want to say its not context free since in the case $i=j=k$ then we have the language $a^nb^nc^n$ which we know is not a CFL.

Answer 1

Look at it this way:

$$L = \{a^ia^jb^jb^kc^kc^i \mid i,j,k > 0\}$$

Which is exactly the same (replacing the sum with concatenation is clearly not a change, and addition is commutative.)