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(Un)decidability of the Emptiness Problem for Multi-dimensional Context-Free Grammars

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Implementation and Application of Automata (CIAA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

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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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Authors and Affiliations

  1. Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University, Zikova 1903/4, 166 36, Prague 6, Czech Republic

    Daniel Průša

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  1. Daniel Průša
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Correspondence to Daniel Průša .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22359-9

  • Online ISBN: 978-3-319-22360-5

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