Real number computation through Gray code embedding. (Q1607300)

We propose an embedding \(G\) of the unit open interval to the set \({0,1}_{\perp,1}^{\omega}\) of infinite sequences of \({0,1}\) with at most one undefined element. This embedding is based on Gray code and it is a topological embedding with a natural topology on \({0,1}_{\perp,1}^{\omega}\). We also define a machine called an indeterministic multihead Type 2 machine which input/output sequences in \({0,1}_{\perp,1}^{\omega}\), and show that the computability notion induced on real functions through the embedding \(G\) is equivalent to the one induced by the signed digit representation and Type 2 machines. We also show that basic algorithms can be expressed naturally with respect to this embedding.