ECCC-Report TR07-051https://eccc.weizmann.ac.il/report/2007/051Comments and Revisions published for TR07-051en-usSat, 16 Jun 2007 18:57:50 +0300
Paper TR07-051
| Bounded Pushdown dimension vs Lempel Ziv information density |
Pilar Albert,
Elvira Mayordomo,
Philippe Moser
https://eccc.weizmann.ac.il/report/2007/051In 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.
Sat, 16 Jun 2007 18:57:50 +0300https://eccc.weizmann.ac.il/report/2007/051