Is the complement of the language generated by $S \to aSbS|\epsilon$ context-free?

Question

How is it possible to prove whether the language $\{a, b\}^{∗} \setminus \{S → ε, S → aSbS\}$ is context free?

Answer 1

The first step is finding a simpler description of the language generated by the grammar $S \to aSbS \mid \epsilon$.

The second step is deducing a description of the complement, which is the language you're actually interested in.

Finally, in order to show that the language is context-free, you can consult our reference question on this topic.