Deterministic Context-Free Languages NOT Closed Under Concatenation

Here we show that deterministic context-free languages (DCFLs) are not closed under concatenation. The idea is to have two languages whose concatenation is the complement of {a^n b^n c^n : n at least 0}, which is not a DCFL.

A deterministic context-free language is the language of a deterministic pushdown automaton (DPDA). The essential idea is that a DPDA is equivalent to a PDA, except that there can only be one "choice" of transition from any state on any input, with anything on the stack. See https://www.youtube.com/watch?v=GzR5FiiIogY&ab_channel=EasyTheory for more details.

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