Bounded Pushdown dimension vs Lempel Ziv information density

Pilar Albert; Elvira Mayordomo; Philippe Moser

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arXiv · 0704.2386

Bounded Pushdown dimension vs Lempel Ziv information density

Pilar Albert·Elvira Mayordomo·Philippe Moser

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Abstract

In this paper we introduce a variant of pushdown dimension called bounded pushdown (BPD) dimension, that measures the density of information contained in a sequence, relative to a BPD automata, i.e. a finite state machine equipped with an extra infinite memory stack, with the additional requirement that every input symbol only allows a bounded number of stack movements. BPD automata are a natural real-time restriction of pushdown automata. We show that BPD dimension is a robust notion by giving an equivalent characterization of BPD dimension in terms of BPD compressors. We then study the relationships between BPD compression, and the standard Lempel-Ziv (LZ) compression algorithm, and show that in contrast to the finite-state compressor case, LZ is not universal for bounded pushdown compressors in a strong sense: we construct a sequence that LZ fails to compress signicantly, but that is compressed by at least a factor 2 by a BPD compressor. As a corollary we obtain a strong separation between finite-state and BPD dimension.

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Pilar Albert, Elvira Mayordomo, Philippe Moser. 2007-04-18. Bounded Pushdown dimension vs Lempel Ziv information density. https://arxiv.org/abs/0704.2386

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