Albert, Pilar and Mayordomo, Elvira and Moser, Philippe (2017) Bounded Pushdown Dimension vs Lempel Ziv Information Density. In: Computabilityand Complexity: Essays Dedicated to Rodney G. Downeyon the Occasion of His 60th Birthday. Lecture Notes in Computer Science (10010). Springer, Cham, Switzerland, pp. 95-114. ISBN 978-3-319-50061-4

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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 significantly, 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.

Item Type:	Book Section
Keywords:	Information lossless compressors; Finite state (bounded pushdown) dimension; Lempel-Ziv compression algorithm;
Academic Unit:	Faculty of Science and Engineering > Computer Science
Item ID:	12014
Identification Number:	https://doi.org/10.1007/978-3-319-50062-1_7
Depositing User:	Philippe Moser
Date Deposited:	12 Dec 2019 15:05
Publisher:	Springer
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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