On the sequential nature of functions

摘要

We discuss the notion of interactive or “on-line” computing as opposed to batchor “off-line” computing, where the input is fully read before any output is produced. The notion of a “maximally defined sequential approximation” is introduced and used to classify the nonsequential functions. The nonsequential functions have varying degrees of sequentiality ranging from the “truly off-line” functions to the “almost sequential” functions, and a dense spectrum is exhibited.