Tree compacting transformations

This paper concerns one aspect of the construction of compact representations ℛ(𝒯) for trees 𝒯 which are instances of an abstract tree data type. The ADT supports operations, on certain trees, built around a top-down traversal primitive, and provides the interface between the second and third stages of a general semantic compression system. The mechanisms used ensure that the time taken to perform all such operations using ℛ(𝒯) is linear with respect to performing the operation directly on 𝒯. They fall into two categories: invertible transformations on 𝒯 which produce an equivalent tree with fewer elements (data or child specifications) than the input form; and the exploitation of statistical variations in the occurrence of data elements to reduce the average space required to represent remaining components