Second-Order Linear-Time Computability with Applications to Computable Analysis.

In this work we put forward a complexity class of type-two linear-time. For such a definition to be meaningful, a detailed protocol for the cost of interactions with functional inputs has to be fixed. This includes some design decisions the defined class is sensible to and we carefully discuss our choices and their implications. We further discuss some properties and examples of operators that are and are not computable in linear-time and nearly linear-time and some applications to computable analysis.