Ein Satz über die Entropie von Untermonoiden (A Theorem on the Entropy of Submonoids)

Abstract Let X be a finite alphabet. For L ⊆ X∗ let ϱL denote the radius of convergence of the structure generating function s L := σ n=0 ∞ card(L∩X n )·t n of the language L. The entropy of L is defined as HL := -logcardX ϱL. We shall prove the following proposition: Theorem. Let L be an arbitrary subset of X∗. Then for every ϵ > 0 there is a finite subset U of L such that HL∗ − HU∗