Closure Properties of Context-Free Languages

Here we look at the five main closure properties--Union, Concatenation, Star, Intersection, and Complement--and show whether they are closed operations for context-free languages. We show that the first three are closed (just by making a simple additional rule to the original grammars), and the other two are not, by being able to produce {a^n b^n c^n : n at least 0}, which is not a CFL.

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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▶ADDITIONAL QUESTIONS◀
1. Can you find an explicit example of a CFL whose complement is not a CFL?
2. Are non-CFLs also closed under the same operations?

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▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.

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