Matching strings in encoded sequences
Probability
2019-12-12 v2 Data Structures and Algorithms
Information Theory
Dynamical Systems
math.IT
Abstract
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the R\'enyi entropy of the source. We apply this result to the zero-inflated contamination model and the stochastic scrabble. In the case of dynamical systems, this problem is equivalent to the shortest distance between two observed orbits and its limiting relationship with the correlation dimension of the pushforward measure. An extension to the shortest distance between orbits for random dynamical systems is also provided.
Cite
@article{arxiv.1903.09625,
title = {Matching strings in encoded sequences},
author = {Adriana Coutinho and Rodrigo Lambert and Jérôme Rousseau},
journal= {arXiv preprint arXiv:1903.09625},
year = {2019}
}