Acta Cybernetica
Petri net algorithms in the theory of matrix grammars
Acta Informatica
Graph-controlled grammars as language acceptors
Journal of Automata, Languages and Combinatorics
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
Nonterminal complexity of programmed grammars
Theoretical Computer Science
From regulated rewriting to computing with membranes: collapsing hierarchies
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
Scattered context grammars generate any recursively enumerable language with two nonterminals
Information Processing Letters
Simple restriction in context-free rewriting
Journal of Computer and System Sciences
Workspace theorems for regular-controlled grammars
Theoretical Computer Science
Nonterminal complexity of tree controlled grammars
Theoretical Computer Science
Language classes generated by tree controlled grammars with bounded nonterminal complexity
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Languages in membrane computing: some details for spiking neural p systems
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Language classes generated by tree controlled grammars with bounded nonterminal complexity
Theoretical Computer Science
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We refine the classical notion of the nonterminal complexity of graph-controlled grammars, programmed grammars, and matrix grammars by also counting, in addition, the number of nonterminal symbols that are actually used in the appearance checking mode. We prove that every recursively enumerable language can be generated by a graph-controlled grammar with only two nonterminal symbols when both symbols are used in the appearance checking mode. This result immediately implies that programmed grammars with three nonterminal symbols where two of them are used in the appearance checking mode as well as matrix grammars with three nonterminal symbols all of them used in the appearance checking mode are computationally complete. Moreover, we prove that matrix grammars with four nonterminal symbols with only two of them being used in the appearance checking mode are computationally complete, too. On the other hand, every language is recursive if it is generated by a graph-controlled grammar with an arbitrary number of nonterminal symbols but only one of the nonterminal symbols being allowed to be used in the appearance checking mode. This implies, in particular, that the result proving the computational completeness of graph-controlled grammars with two nonterminal symbols and both of them being used in the appearance checking mode is already optimal with respect to the overall number of nonterminal symbols as well as with respect to the number of nonterminal symbols used in the appearance checking mode, too. Finally, we also investigate in more detail the computational power of several language families which are generated by graph-controlled, programmed grammars or matrix grammars, respectively, with a very small number of nonterminal symbols and therefore are proper subfamilies of the family of recursively enumerable languages.