Pebble-depth

In this paper we introduce a new feasible notion of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of prefixes of infinite sequences from the perspective of finite-state transducers and pebb...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1009; p. 114638
Main Authors: Jordon, Liam, Maguire, Phil, Moser, Philippe
Format: Journal Article
Language:English
Published: Elsevier B.V 12.09.2024
Subjects:
Compression algorithms
Kolmogorov complexity
Logical depth
Pebble transducer
Logical depth
Pebble transducer
Compression algorithms
Kolmogorov complexity
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:In this paper we introduce a new feasible notion of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of prefixes of infinite sequences from the perspective of finite-state transducers and pebble transducers. Our notion of pebble-depth satisfies the four fundamental properties of depth: i.e. deep sequences exist, trivial sequences are not deep, random sequences are not deep, and the existence of a slow growth law type result. We also compare pebble-depth to other depth notions based on finite-state transducers, pushdown compressors, and the Lempel-Ziv 78 compression algorithm. We first demonstrate how there exists a normal pebble-deep sequence even though there is no normal finite-state-deep sequence. We next build a sequence that has a pebble-depth level of roughly 1, a pushdown-depth level of roughly 1/2 and a finite-state-depth level of roughly 0. We then build a sequence that has a pebble-depth level of roughly 1/2 and a Lempel-Ziv-depth level of roughly 0.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114638