In this paper we study several notions of approximability of functions in the framework of the BSS model. Denoting with ϕ M δ the function computed by a BSS machine M when its comparisons are against −δ rather than 0, we study classes of functions f for which ϕ M δ → f in some sense (pointwise, uniformly, etc.). The main equivalence results show that this notion coincides with Type 2 computability when the convergence speed is recursively bounded. Finally, we study the possibility of extending these results to computations over Archimedean fields.
KeywordsStrict Inequality Recursive Function Computable Function Approximable Function Partial Algebra
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