, where A trio is a family of languages closed under homomorphisms that do not introduce the empty word, inverse homomorphisms, and intersections with a regular language.
The following are some simple results from the study of abstract families of languages.
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.
[2] Seymour Ginsburg of the University of Southern California and Sheila Greibach of Harvard University presented the first AFL theory paper at the IEEE Eighth Annual Symposium on Switching and Automata Theory in 1967.