Non Sequential Recursive Pair Substitution: Some Rigorous Results

Abstract

We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding natural action on measures and we prove that the iterated measure becomes asymptotically Markov. This certify the effectiveness of NSRPS as a tool for data compression and entropy estimation.

20 pages

References in corpus (7)

• Entropy estimation of symbol sequences
• Heuristic Segmentation of a Nonstationary Time Series
• Data compression and learning in time sequences analysis
• Entropy of Pseudo Random Number Generators
• Data Compression and Entropy Estimates by Non-sequential Recursive Pair Substitution
• Artificial Sequences and Complexity Measures
• SYNTAX: A computer program to compress a sequence and to estimate its information content

Cited by in corpus (5)

• Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems
• Problems with information theoretic approaches to causal learning
• R-grams: Unsupervised Learning of Semantic Units in Natural Language
• Encryption dynamics and avalanche parameter for "delayed dynamics"-based cryptosystems
• Relative entropy via non-sequential recursive pair substitutions