Constructing PDA to accept language { $a^i b^j c^k \mid i,j,k \geq0, i+2k = j$ }
Hint: The PDA has three phases: an $a$ phase, a $b$ phase and a $c$ phase. Your goal in the $a$ phase is to "compute" $i$ by strong an appropriate load on the stack. Your goal in the $b$ phase is to compute $j-i$. Finally, your goal in the $c$ phase is to compare $j-i$ to $2k$.