Entropy Bounds for Grammar-Based Tree Compressors

The definition of k
^th
-order empirical entropy of strings is extended to node-labeled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to yield binary tree encodings of size bounded by the k
^th
-order empirical entropy plus some lower order terms. This generalizes recent results for grammar-based string compression to grammar-based tree compression. A long version of this paper can be found in [11].