Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
On the number of nonterminals in linear conjunctive grammars
Theoretical Computer Science
Information and Computation
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
Theory of Computing Systems - Special Issue: Symposium on Computer Science, Guest Editors: Sergei Artemov, Volker Diekert and Dima Grigoriev
Fast parsing for Boolean grammars: a generalization of Valiant's algorithm
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Complexity of Equations over Sets of Natural Numbers
Theory of Computing Systems
One-Nonterminal Conjunctive Grammars over a Unary Alphabet
Theory of Computing Systems
On the expressive power of univariate equations over sets of natural numbers
Information and Computation
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It is demonstrated that the family of languages generated by unambiguous conjunctive grammars with 1 nonterminal symbol is strictly included in the languages generated by 2-nonterminal grammars, which is in turn a proper subset of the family generated using 3 or more nonterminal symbols. This hierarchy is established by considering grammars over a one-letter alphabet, for which it is shown that 1-nonterminal grammars generate only regular languages, 2-nonterminal grammars generate some non-regular languages, but all of them have upper density zero, while 3-nonterminal grammars may generate some non-regular languages of non-zero density. It is also shown that the equivalence problem for 2-nonterminal grammars is undecidable.