Formal Definitions
A formal language is a set for which there exists a finite set of abstract symbols such that, where * is the Kleene star operation.
A family of languages is an ordered pair, where
- is an infinite set of symbols;
- is a set of formal languages;
- For each in there exists a finite subset ⊂ such that ⊆ ; and
- ≠ Ø for some in .
A trio is a family of languages closed under e-free homomorphism, inverse homomorphism, and intersection with regular language.
A full trio, also called a cone, is a trio closed under arbitrary homomorphism.
A (full) semi-AFL is a (full) trio closed under union.
A (full) AFL is a (full) semi-AFL closed under concatenation and the Kleene plus.
Read more about this topic: Abstract Family Of Languages
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