A NOTE ON BINARY GRAMMATICAL CODES OF TREES

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 c ode-word is precisely the number of leaves of the coded tree. Such cod es 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 [1]. In this n ote we present two topics related to binary grammatical codes. The fir st topic (see Section 2) is grammatical codes of binary trees with a m inimal code alphabet. It is shown that the only binary codes that are minimal in this sense are the so-called ''strict'' binary codes (as co nsidered in [3]).The second topic (see Section 3) concerns the extensi on of binary grammatical codes to grammatical codes for trees of arbit rary 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.