# Paper with proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ is not Deterministic Context Free?

These lecture slides sketch a proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ cannot be accepted by any Deterministic Pushdown Automaton. Unfortunately, the slides give no references as to where the proof comes from.

I was wondering, does anybody know of an academic paper or textbook that gives a full proof? I'd love to be able to cite it, but I haven't been able to find one.

• As a note: the slides follow the same argument as the one I use in a related question on Pumping Lemma's for deterministic CFL. (This is a non-pumping argument of course.) – Hendrik Jan May 30 '13 at 8:14