# Closure Properties

Learn about the closure properties of deterministic and nondeterministic context-free languages.

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## Closure properties of nondeterministic CFLs

Since there is a difference between deterministic and non-deterministic context-free languages, there are differences in their closure properties. We first develop the closure properties for non-deterministic context-free languages, using CFG-based arguments. “Context-free-ness” is preserved under the following operations:

- Union.
- Concatenation.
- Kleene star.
- Regular intersection (intersection with a regular language).
- Regular union (union with a regular language).

Suppose $S_1$ and $S_2$ are the respective start variables for context-free languages $L_1$ and $L_2$. We can form a CFG for $L_1 \cup \; L_2$ as follows:

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