Summary
A two-dimensional (2-d) language is a set of 2-d arrays of symbols, whose theories give the mathematical foundation for 2-d information processing. There are various formal methods for treating 2-d languages. They can be classified into two types, i.e., methods based on 2-d automata, and those of 2-d grammars (or pattern generating systems).
In the first section, basic notions on 2-d languages are given. Then, in the second and third sections, automata-theoretic approaches and 2-d grammar formalisms are described and discussed. Fundamental results on them and some open problems are surveyed. Comparison with the one-dimensional case is also made.
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Morita, K. (2004). Two-Dimensional Languages. In: MartÃn-Vide, C., Mitrana, V., Păun, G. (eds) Formal Languages and Applications. Studies in Fuzziness and Soft Computing, vol 148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39886-8_22
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DOI: https://doi.org/10.1007/978-3-540-39886-8_22
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