Acceptance for Context-Free Grammars is Decidable

Here we show that A_CFG is decidable. The main method of proof is the fact that any CFG in Chomsky Normal Form (CNF) will have all derivations of a string w of length 2|w|-1, if w is non-empty. The basic idea then is to try all possible derivations of that length. If any of them work, accept; otherwise, reject.

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    • Context-Free Grammars (CFG) and Conte...   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.