4 papers · 1 filter
A Markov-Chain Characterization of Finite-State Dimension and a Generalization of Agafonov's Theorem
Laurent Bienvenu, Hugo Gimbert, Subin Pulari
Finite-state dimension quantifies the asymptotic rate of information in an infinite sequence as perceived by finite automata. For a fixed alphabet, the infinite sequences that have…
Point-to-set Principle and Constructive Dimension Faithfulness
Satyadev Nandakumar, Subin Pulari, Akhil S
Hausdorff -dimension is a notion of Hausdorff dimension developed using a restricted class of coverings of a set. We introduce an effective version of Hausdorff -dimension, w…
Finite-State Relative Dimension, dimensions of A. P. subsequences and a Finite-State van Lambalgen's theorem
Satyadev Nandakumar, Subin Pulari, Akhil S
Finite-state dimension (Dai, Lathrop, Lutz, and Mayordomo (2004)) quantifies the information rate in an infinite sequence as measured by finite-state automata. In this paper, we de…
Real numbers equally compressible in every base
Satyadev Nandakumar, Subin Pulari
This work solves an open question in finite-state compressibility posed by Lutz and Mayordomo about compressibility of real numbers in different bases. Finite-state compressibility…