On the Complexity of Real Functions

Abstract

We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS computability [Blum, Cucker, Shub, Smale 1998], and bit computability in the tradition of computable analysis [Weihrauch 2000] as it relies on the latter but allows some discontinuities and multiple values.