Pushdown Compression

TL;DR

This paper introduces pushdown compressors based on pushdown transducers for XML data, compares their performance with Lempel-Ziv, and proves their incomparability in asymptotic compression ratios.

Contribution

It formalizes pushdown compressors using pushdown transducers and analyzes their performance relative to Lempel-Ziv without source assumptions.

Findings

Lempel-Ziv outperforms finite-state compressors on all sequences.

Pushdown compressors are shown to be incomparable with Lempel-Ziv in asymptotic ratio.

The model allows formal analysis of stack-based compression schemes.

Abstract

The pressing need for eficient compression schemes for XML documents has recently been focused on stack computation [6, 9], and in particular calls for a formulation of information-lossless stack or pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms. In this paper we introduce the model of pushdown compressor, based on pushdown transducers that compute a single injective function while keeping the widest generality regarding stack computation. The celebrated Lempel-Ziv algorithm LZ78 [10] was introduced as a general purpose compression algorithm that outperforms finite-state compressors on all sequences. We compare the performance of the Lempel-Ziv algorithm with that of the pushdown compressors, or compression algorithms that can be implemented with a pushdown transducer. This comparison is made without any a priori assumption on the data's source and considering the asymptotic compression ratio for infinite sequences. We prove that Lempel-Ziv is incomparable with pushdown compressors.