### Some Algebraic Properties of Regular Tree Transformations

#### Abstract

A regular generalized hypersubstitutions is a mapping from \(\{f_{i} \mid i \in I \}\) to \(W_{\tau}(X)\) such that for every \(i \in I\), each of the variables \(x_{1},x_{2}, \ldots , x_{n_{i}}\) occur in \(\hat{\sigma}[f_{i}(x_{1}, x_{2},\ldots ,x_{n_{i}})]\). We use the extension of regular generalized hypersubstitutions to define tree transformations which is useful for abstract data type specifications in Theoretical Computer Science. In this paper, we study some algebraic properties of tree transformations.

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DOI: http://dx.doi.org/10.26713%2Fcma.v10i4.1273

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