Non Sequential Recursive Pair Substitution: Some Rigorous Results

TL;DR

This paper provides rigorous mathematical results on the NSRPS method, demonstrating its effectiveness in data compression and entropy estimation by showing that iterated measures become asymptotically Markov.

Contribution

It establishes a formal connection between NSRPS actions on strings and measures, proving asymptotic Markovianity of the iterated measure, thus advancing theoretical understanding.

Findings

NSRPS measure becomes asymptotically Markov

Validates NSRPS as a data compression tool

Provides rigorous mathematical foundation for NSRPS

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.