On Mealy-Moore coding and images of Markov measures
Rostislav Grigorchuk, Roman Kogan, Yaroslav Vorobets
TL;DR
This paper investigates how Markov measures transform under Mealy automata, identifying conditions for absolute continuity or singularity of the resulting measures and analyzing statistical properties of generic sequences.
Contribution
It provides new conditions for the absolute continuity or singularity of measures under Mealy automata transformations and explores statistical properties of generic sequences.
Findings
Conditions for absolute continuity and singularity of measures
Characterization of statistical properties of images of generic sequences
Analysis of Mealy automata effects on Markov measures
Abstract
We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine statistical properties of the image of a generic sequence.
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Taxonomy
TopicsMathematical Dynamics and Fractals · semigroups and automata theory · Computability, Logic, AI Algorithms