Entropy Bounds for Grammar-Based Tree Compressors

01/10/2019

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by   Danny Hucke, et al.

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The definition of k^th-order empirical entropy of strings is extended to node labelled 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.