# Contextual Array Grammars with Matrix and Regular Control

Abstract : We investigate the computational power of d-dimensional contextual array grammars with matrix control and regular control languages. For $d\ge 2$, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. Yet in the 1-dimensional case, for a one-letter alphabet, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages coincides with the family of regular 1-dimensional array languages, whereas for alphabets with more than one letter, we obtain the array images of the linear languages.
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https://hal.inria.fr/hal-01633942
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Henning Fernau, Rudolf Freund, Rani Siromoney, K. Subramanian. Contextual Array Grammars with Matrix and Regular Control. 18th International Workshop on Descriptional Complexity of Formal Systems (DCFS), Jul 2016, Bucharest, Romania. pp.98-110, ⟨10.1007/978-3-319-41114-9_8⟩. ⟨hal-01633942⟩

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