Abstract
We study how dimensionality and form of context-free productions affect the power of multi-dimensional context-free grammars over unary alphabets. Attention is paid to the emptiness decision problem. It is an open question whether or not it is decidable for two-dimensional Kolam type context-free grammars of Siromoney. We show that the undecidability can be proved in the three-dimensional setting. For the two-dimensional variant, we present several results revealing that the process of generating is still much more complex than that one of the classical one-dimensional context-free grammar.
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Acknowledgement
The author would like to thank Markus Holzer for his suggestions that became the basis for this paper. This work was supported by the Czech Science Foundation under grant no. 15-04960S.
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Průša, D. (2015). (Un)decidability of the Emptiness Problem for Multi-dimensional Context-Free Grammars. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_21
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DOI: https://doi.org/10.1007/978-3-319-22360-5_21
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