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10th Annual Symposium on Switching and Automata Theory (swat 1969) (1969)
Oct. 15, 1969 to Oct. 17, 1969
ISSN: 0272-4847
pp: 222-230
A superAFL is a family of languages closed under union with unitary sets, intersection with regular sets, and nested iterated substitution and containing at least one nonunitary set. Every superAFL is a full AFL containing all context-free languages. If L is a full principal AFL, then S∞(L, the least superAFL containing L, is full principal. If L is not substitution closed, the substitution closure of L is properly contained in S∞ (L). The index languages form a superAFL which is not the least superAFL containing the one way stack languages. If L has a decidable emptiness problem, so does S∞ (L). If Ds is an AFA, L=L (Ds) and Dw is the family of machines whose data structure is a pushdown store of tapes of Ds, then L (Dw) = S∞(L) if and only if Ds is nontrivial. If Ds is uniformly erasable and L(Ds) has a decidable emptiness problem, then it is decidable if a member of Dw is finitely nested.

S. A. Greibach, "Full AFLS and nested iterated substitution," 10th Annual Symposium on Switching and Automata Theory (swat 1969)(FOCS), vol. 00, no. , pp. 222-230, 1969.
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