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
Famous quotes containing the words formal and/or definitions:
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—Horace Walpole (1717–1797)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)