Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computable classifications of continuous, transducer, and regular
  functions   We develop a systematic algorithmic framework that unites global and local
classification problems for functional separable spaces and apply it to attack
classification problems concerning the Banach space C[0,1] of real-valued
continuous functions on the unit interval. We prove that the classification
problem for continuous (binary) regular functions among almost everywhere
linear, pointwise linear-time Lipshitz functions is $\Sigma^0_2$-complete. We
show that a function $f\colon [0,1] \rightarrow \mathbb{R}$ is (binary)
transducer if and only if it is continuous regular; interestingly, this
peculiar and nontrivial fact was overlooked by experts in automata theory. As
one of many consequences, our $\Sigma^0_2$-completeness result covers the class
of transducer functions as well. Finally, we show that the Banach space
$C[0,1]$ 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.

13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an