Regular languages
Suppose A and B are regular languages
from the alphabet Σ.
- A ∪ B is regular.
- A ∩ B is regular.
- A ∘ B is regular.
- A* is regular.
- Σ - A is regular.
Look at David Plaisted’s Finite Automata and Regular Expressions
for more detail.
Context-Free Languages
Suppose A and B are context-free languages
from the alphabet Σ
- A ∪ B is context-free.
- A ∘ B is context-free.
- A* is context-free.
The intersection of a context-free language and a regular language
is context-free.
Problem 2.2 shows that context-free languages are not closed under
intersection and complementation.
Look at David Plaisted’s Closure Properties of Context-Free Languages
for more detail.