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We study verifiable outsourcing of computation in a model where the verifier has black-box access to the function being computed. We introduce the problem of oracle-aided batch verification of computation (OBVC) for a function class $$\mathcal{F}$$. This allows a verifier to efficiently verify the correctness of any $$f \in \mathcal{F}$$ evaluated on a batch of $$n$$ instances $$x_1, \ldots, x_n$$, while only making $$\lambda$$ calls to an oracle for $$f$$ (along with $$O(n \lambda)$$ calls to low-complexity helper oracles), for security parameter $$\lambda$$. We obtain the following positive and negative results: - We build OBVC protocols for the class of all functions that admit {\em random-self-reductions}. Some of our protocols rely on homomorphic encryption schemes. - We show that there cannot exist OBVC schemes for the class of all functions mapping $$\lambda$$-bit inputs to $$\lambda$$-bit outputs, for any $$n = \mathsf{poly}(\lambda)$$.