A note on binary grammatical codes of trees

Andrzej Ehrenfeucht, Paulien ten Pas, Grzegorz Rozenberg
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Grammatical codes of trees provide a way to encode ordered trees into strings over a finite alphabet in such a way that the length of each code-word is precisely the number of leaves of the coded tree. Such codes are grammatical because they result by applying production rules of a grammar G to a tree t which becomes then a derivation tree t' in G and the yeild of this derivation tree t' becomes the code-word for t. Grammatical codes were investigated in [2,3], see also [l]. In this note we
more &raquo; ... ent two topics related to binary grammatical codes. The first topic (see Section 2) is grammatical codes of binary trees with a minimal code alphabet. It is shown that the only binary codes that are minimal in this sense are the so-called "strict" binary codes (as considered in [S]). The second topic (see Section 3) concerns the extension of binary grammatical codes to grammatical codes for trees of arbitrary degree. We make comparisons between classes of codes obtained in this way and the classes from [2, 3] . In Section 1 we recall (from [2,3]) some notions and results concerning grammatical codes.
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