Language Properties
- UNION of two NON-Regular languages can be Regular.
- E.g. a non-regular language and its compliment, is Σ*, which is regular.
- INTERSECTION of NON-Regular language and Regular language can be regular.
- E.g. classic non-regular language and empty set results in empty set, which is regular
- L² is the language concatenated with itself. L¹ is the language itself. L° is the language containing only the lambda = {λ}
- I was wondering why L° = {λ} and not L° = ∅ but I found it can’t be ∅ since if you concatenate ∅ with L¹ for example, you would get ∅ and not L¹.
Grammars
- A grammar that produces words with no terminals, is simply the grammar for ∅, even if it looks fancy.
- E.g. S -> SS | Sa | aS
- E.g. S -> aA | a, A -> AbA produces only the language {a} since the A variable doesn’t produce anything with only terminals.
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