Abstract
We consider formal sequences of d-dimensional vectors and symbols representing d-dimensional arrays and introduce the operations of catenation as well as iterated catenation of these formal sequences (d-dimensional formal arrays). Together with the usual set union, these operations allow us to define d-dimensional regular array expressions and thus to develop an algebraic representation of regular array languages generated by specific d-dimensional array grammars. In that way, specific infinite regular array languages allow for a finite representation as regular array expressions. Whereas, in general, it is undecidable whether the array language generated by a given regular array grammar is empty, finite or infinite, for these specific regular array grammars, these questions are decidable.
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© 2000 Springer-Verlag London Limited
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Freund, R., Mateescu, A., Salomaa, A. (2000). Algebraic Representations of Regular Array Languages. In: Finite Versus Infinite. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0751-4_9
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DOI: https://doi.org/10.1007/978-1-4471-0751-4_9
Publisher Name: Springer, London
Print ISBN: 978-1-85233-251-8
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