Models of computation for partial functions on the reals

We compare models of computation for partial functions f:R⇀R. We consider four models: two concrete (Grzegorczyk–Lacombe and tracking computability), one abstract (approximability by a While program with “countable choice”) and a new hybrid model: multipolynomial approximability. We show that these four models are equivalent, under the two assumptions:(1)the domain of f is the union of an effective exhaustion, i.e. a sequence of “stages”, each …