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Journal Articles Theoretical Computer Science Year : 2007

Local Rule Substitutions and Stepped Surfaces

Thomas Fernique
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Abstract

Substitutions on words, \emph{i.e.}, non-erasing morphisms of the free monoid, are simple combinatorial objects which produce infinite words by replacing iteratively letters by words. This paper introduces a notion of substitution acting on multi-dimensional words, namely the \emph{local rule substitutions}. Roughly speaking, \emph{local rules} play for multi-dimensional words the role played by the concatenation product for substitutions on words. We then particularly focus on the local rule substitutions which act on the $2$-dimensional words coding \emph{stepped surfaces}, and we show that a wide class of them can be derived from \emph{generalized substitutions}.
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Dates and versions

lirmm-00149362 , version 1 (25-05-2007)

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Thomas Fernique. Local Rule Substitutions and Stepped Surfaces. Theoretical Computer Science, 2007, 380, pp.317-329. ⟨10.1016/j.tcs.2007.03.021⟩. ⟨lirmm-00149362⟩
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