Denseness of volatile and nonvolatile sequences of functions

Abstract: In a paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, ( f_n \colon { -1,1 }^n \to { -1,1 } ) were introduced. We continue their study of how these definitions relate to noise stability and noise sensitivity. Our main results are that the set of volatile sequences of Boolean functions is a natural way "dense" in the set of all sequences of Boolean functions, and that the set of non-volatile Boolean sequences is not "dense" in the set of noise stable sequences of Boolean functions.