We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear, pointwise linear-time Lipschitz functions is -complete. (Every regular function is pointwise linear-time Lipschitz.) We show that a function is (binary) transducer if and only if it is continuous regular. As one of many consequences, our -completeness result covers the class of transducer functions as well. Finally, we show that the Banach space of real-valued continuous functions admits an arithmetical classification among separable Banach spaces. Our proofs combine methods of abstract computability theory, automata theory, and functional analysis.     «

We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear, pointwise linear-time Lipschitz functions is -complete. (Every regular function is pointwise linear-time Lipschitz.) We show that a function is (binary) transducer if and only if it is continuous regular. As one of many consequences, our -completeness result co...     »