If both $L$ and $\overline{L}$ are context-free, is $L$ necessarily regular?
2026-03-25 04:37:45.1774413465
If a language and its complement are context-free, is it regular?
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Every deterministic context-free language satisfies this, since the deterministic context-free languages are closed under complementation. Not all deterministic context-free languages are regular, for example $\{ a^n b^n : n \geq 0 \}$ isn't.