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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Hyperbolic tilings and formal language theory
TL;DR: In this article, the authors show an application of this device to the characterization of contour words of a family of bounded domains in many tilings of the hyperbolic plane.
Journal ArticleDOI
Tree Adjoining Languages and Multipushdown Languages
TL;DR: It is proved that 2-pdl can be characterized exactly as the smallest full super-AFL that includes 2- pdl , the class of languages generated by tag .
Posted ContentDOI
A B\"uchi-Elgot-Trakhtenbrot theorem for automata with MSO graph storage
Joost Engelfriet,Heiko Vogler +1 more
TL;DR: It is proved that (i) each MSO graph transduction can be used as storage transformation in an MSOgraph storage type, (ii) every automatic storage type is MSO-expressible, and (iii) the pushdown operator on storage types preserves the property of MSO -expressibility.
Journal ArticleDOI
Continuous operations on languages
TL;DR: Most of the operations of interest in language theory are continuous in a certain technical sense, but there always exist infinite sets of languages that areindependent in the sense that no language in such a set can be generated from the other languages in the set by the operations in question.
Journal ArticleDOI
Principal abstract families of weighted tree languages
Zoltán Fülöp,Heiko Vogler +1 more
TL;DR: It is shown that the class of weighted tree languages generated by semiring-weighted regular tree grammars with storage where the semiring is complete is a principal abstract family of weighted Tree languages provided that the semired is commutative, the rank of symbols occurring in trees is bounded by a global parameter, and the storage is finitely encoded and contains a reset instruction.
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.