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.
Work supported by Bundesministerium für Bildung, Wissenschaft und Kunst, Austria, grant GZ 55.300/269-VII/D/5a/2000 and by a grant of the NATO Science Committee, Spain, 2000-2001
Acknowledgement
We gratefully acknowledge some interesting discussions with Henning Fernau.
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Freund, R., Păun, G. (2001). On the Number of Non-Terminal Symbols in Graph-Controlled, Programmed and Matrix Grammars. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_14
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DOI: https://doi.org/10.1007/3-540-45132-3_14
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