On the Number of Non-Terminal Symbols in Graph-Controlled, Programmed and Matrix Grammars

Abstract

We improve the results elaborated in [6] on the number of non-terminal symbols needed in matrix grammars, programmed grammars, and graph-controlled grammars with appearance checking for generating arbitrary recursively enumerable languages. Of special interest is the result that the number of non-terminal symbols used in the appearance checking mode can be restricted to two. In the case of graph controlled (and programmed grammars) with appearance checking also the number of non-terminal symbols can be reduced to three (and four, respectively); in the case of matrix grammars with appearance checking we either need four non-terminal symbols with three of them being used in the appearance checking mode or else again we only need two non-terminal symbols being used in the appearance checking mode, but in that case we cannot bound the total number of non-terminal symbols.KeywordsTuring MachineSentential FormInitial RuleTerminal SymbolRegister MachineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.