May 11, 2023 · In this paper, we define a relative version of finite-state dimension. The finite-state relative dimension dim_{FS}^Y(X) of a sequence X ...

Mar 6, 2024 · Finite-state dimension, introduced by Dai, Lathrop, Lutz and Mayordomo [1] quantifies the information rate in an infinite sequence as ...

In this work, we introduce a notion of the relative finite-state dimension of a sequence X with respect to any arbitrary sequence Y.

Jan 1, 2023 · In this work, we introduce a notion of the relative finite-state dimension of a sequence X with respect to any arbitrary sequence Y.

May 11, 2023 · We derive inequalities relating the dimension of a sequence to the relative dimension of its subsequences along any arithmetic progression (A.P.) ...

These enable us to obtain a strengthening of Wall's Theorem on the normality of A. P. subsequences of a normal sequence, in terms of relative dimension. In ...

In this paper, we define a relative version of finite-state dimension. The finite-state relative dimension dimFSY(X) of a sequence X relative to Y is the finite ...

Mar 21, 2024 · In this paper we extend van Lambalgen's Theorem by considering the join of infinitely many reals which are random relative to each other. In ...

Finite-state relative dimension, dimensions of A. P. subsequences and a finite-state van Lambalgen's theorem. https://doi.org/10.1016/j.ic.2024.105156.

Finite-State Relative Dimension, Dimensions of AP Subsequences and a Finite-State van Lambalgen's Theorem. S. Nandakumar, S. Pulari, and A. S.