Measures of $\e$-complexity
V.Afraimovich, L.Glebsky
TL;DR
This paper investigates measures related to $ ext{ extsterling}$-complexity, demonstrating the equivalence of two different definitions based on $ ext{ extsterling}$-separability and $ ext{ extsterling}$-nets, with implications for complexity theory.
Contribution
It establishes the equivalence between $ ext{ extsterling}$-complexity measures defined via $ ext{ extsterling}$-separability and $ ext{ extsterling}$-nets, clarifying their relationship.
Findings
Proves the equivalence of two $ ext{ extsterling}$-complexity measures.
Links $ ext{ extsterling}$-separability with $ ext{ extsterling}$-nets.
Provides insights into complexity measurement methods.
Abstract
We study some measures which are related to the notion of the -complexity. We prove that measure of -complexity defined on the base of the notion of -separability is equivalent to the dual measure that is defined through -nets. Keywords: Complexity, Separability, Bernoulli measure
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Taxonomy
TopicsMathematical Dynamics and Fractals · semigroups and automata theory · Computability, Logic, AI Algorithms