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We compare models of computation for partial functions f : R ⇀ R. We consider four models: two concrete (Grzegor-czyk-Lacombe and tracking computability), one abstract (approx-imability 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… (More)

We give some characterizations of semicomputability of sets of reals by programs in certain While programming languages over a topological partial algebra of reals. We show that such sets are semicomputable if and only if they are one of the following: (i) unions of effective sequences of disjoint algebraic open intervals; (ii) unions of effective sequences… (More)

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