3 research outputs found
Generating All Permutations by Context-Free Grammars in Greibach Normal Form
We consider context-free grammars in Greibach normal form and, particularly, in Greibach -form () which generates the finite language of all strings that are permutations of different symbols (). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of as functions of . As in the case of Chomsky normal form these descriptional complexity measures grow faster than any polynomial function
Merging two Hierarchies of Internal Contextual Grammars with Subregular Selection
In this paper, we continue the research on the power of contextual grammars
with selection languages from subfamilies of the family of regular languages.
In the past, two independent hierarchies have been obtained for external and
internal contextual grammars, one based on selection languages defined by
structural properties (finite, monoidal, nilpotent, combinational, definite,
ordered, non-counting, power-separating, suffix-closed, commutative, circular,
or union-free languages), the other one based on selection languages defined by
resources (number of non-terminal symbols, production rules, or states needed
for generating or accepting them). In a previous paper, the language families
of these hierarchies for external contextual grammars were compared and the
hierarchies merged. In the present paper, we compare the language families of
these hierarchies for internal contextual grammars and merge these hierarchies.Comment: In Proceedings NCMA 2023, arXiv:2309.07333. arXiv admin note: text
overlap with arXiv:2309.02768, arXiv:2208.1472
Strictly Locally Testable and Resources Restricted Control Languages in Tree-Controlled Grammars
Tree-controlled grammars are context-free grammars where the derivation
process is controlled in such a way that every word on a level of the
derivation tree must belong to a certain control language. We investigate the
generative capacity of such tree-controlled grammars where the control
languages are special regular sets, especially strictly locally testable
languages or languages restricted by resources of the generation (number of
non-terminal symbols or production rules) or acceptance (number of states).
Furthermore, the set theoretic inclusion relations of these subregular language
families themselves are studied.Comment: In Proceedings AFL 2023, arXiv:2309.0112