Asymptotic Density for Equivalence

It was already proved that the asymptotic density for k=1 exists for all binary connectives except equivalence. In this paper we prove that for every k there are exactly two accumulation points for the language based on equivalence: 0, 1/2k−1 for asymptotic density and 1/2k−1(4k+1), 4k/2k−1(4k+1) for cumulative asymptotic density.