Some Families of Languages
The following are some simple results from the study of abstract families of languages.
Within the Chomsky hierarchy, the regular languages, the context-free languages, and the recursively enumerable languages are all full AFLs. However, the context sensitive languages and the recursive languages are AFLs, but not full AFLs because they are not closed under arbitrary homomorphisms.
The family of regular languages are contained within any cone (full trio). Other categories of abstract families are identifiable by closure under other operations such as shuffle, reversal, or substitution.
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