Undecidability of the Universality Problem for Context-Free Grammars 🚫

Here we show that the "universality" problem for context-free grammars is undecidable. It is similar to the E_LBA video but we instead embed strings NOT encoding "reversed" accepting computation histories into the CFG.

What is a context-free grammar? It is a set of 4 items: a set of "variables," a set of "terminals," a "start variable," and a set of rules. Each rule must involve a single variable on its "left side", and any combination of variables and terminals on its right side. See https://www.youtube.com/watch?v=h1OSmLSacNA&ab_channel=EasyTheory for more details.

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.