Full AFLs and nested iterated substitution
TLDR
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 containing all context-free languages.Abstract:
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 Ŝ∞(L), the least superAFL containing L, is full principal If L is not substitution closed, the substitution closure of L is properly contained in Ŝ∞(L) The indexed 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 Ŝ∞(L) IfDs 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(Ds) = Ŝ∞(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 nestedread more
Citations
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Book ChapterDOI
Regular sets of higher-order pushdown stacks
TL;DR: It is proved that any regular set of level k stacks admits a normalized representation and it is used to show that the regular sets of a given level form an effective Boolean algebra.
Journal ArticleDOI
Fibonacci words, hyperbolic tilings and grossone
TL;DR: The contribution of the theory of grossone to the study of infinite Fibonacci words is studied, combining this tool with the help of a particular tiling of the hyperbolic plane: the heptagrid.
Journal ArticleDOI
Algebraic aspects of families of fuzzy languages
TL;DR: In this article, the concept of full abstract family of fuzzy languages or full AFFL was introduced, which is the fuzzy counterpart of the notion of fuzzy abstract families of languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages.
Journal ArticleDOI
Formal Languages: Origins and Directions
TL;DR: It is observed that the same important ideas emerged independently for the automatic analysis and translation of both natural and artificial languages in the 1950s and early 1960s.
Posted Content
Context-Free Grammars with Storage
TL;DR: The context-free S languages can be obtained from the deterministic one-way S automaton languages by way of the delta operations on languages, introduced in this paper.
References
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Journal ArticleDOI
Indexed Grammars—An Extension of Context-Free Grammars
TL;DR: A new type of grammar for generating formal languages, called an indexed grammar, is presented, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages.
Proceedings ArticleDOI
Grammars with macro-like productions
TL;DR: Two new classes of grammars based on programming macros are studied, one of which is IO but not OI and the other OI but not IO, showing that neither class contains the other.
Journal ArticleDOI
One-way stack automata
TL;DR: A number of operations which either preserve sets accepted by one-way stack automata or preserve setsaccepted by deterministic one- way stack Automata are presented.
Journal ArticleDOI
Checking automata and one-way stack languages
TL;DR: The quasi-real-time one- way stack languages are not a full AFL but are a proper subAFL of the one-way stack languages, which properly include the stack languages.