I am trying to generate a Pushdown Automaton that accepts the strings of the language $L=\{a^i b^j c^k, i + k \ne j\}$.
From this I know that the following situations can occur: $i + k < j$ or $i + k > j$ which seems to mean that I will be merging two different automata, but I am not sure how to go about doing so due to the given condition.
How do I go about solving?