We study the power of big products for computing multivariate polynomials in a Valiant-like framework. More precisely, we define a new class VIIP~o as the set of families of polynomials that are exponential products of easily computable polynomials. We investigate the consequences of the hypothesis that these big products are themselves easily computable. For instance, this hypothesis would imply that the nonuniform versions of P and NP coincide.
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