Binary Tree Code Words as Context-Free Languages

Given a binary tree coding system, the set of valid code words of all binary trees can be considered as a context-free language over the alphabet used in the coding system. The complexity of the language obtained varies from one coding system to another. Xiang, Tang and Ushijima have recently proved some properties of such languages. We show that their results can be more easily proved by noticing the form of the generating grammar in question. Namely, in the simplest cases the language obtained is a left Szilard language, a very simple deterministic language. Moreover, we prove some new results concerning the 'binary tree languages'.

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