(1) $L_1 = \{a^ib^{i+j}c^j|i,j\geq 0\} $(2) $L_2 = \{xy | x,y \in \{0,1\}^*, x \neq y, |x| = |y| \}$I doubt that $L_1$ is CFL. I've been trying to go with the string $s$ = $a^pb^{2p}c^p$. Thus, we can write $s$ as $uvxyz$. Now I'm trying to show $uv^2xy^2z$ is not in $L_1$. I really have no idea how to approach (2). And if it is context free, how in the world would you draw a pda?
Determine whether two languages are context free
context free;pushdown automata
For the first one, $$L_1 = \{a^i,b^{i+j}c^j \mid i,j \geq 0 \} $$Here's an rough idea of the algorithm:read off the all '$a$'s and push $a$ into the stackupon seeing a '$b$', pop the '$a$'s till the stack is emptythen again as long as reading '$b$'s keep pushing $b$ into the stackon seeing a $c$, start popping the stack until empty.For the second one, Please see my answer here, The other answer is equally good (perhaps even better and simpler) than mine.