In this paper we construct an oracle under which the polynomial hierarchy is infinite but there are non-invertible polynomial time computable multivalued onto functions.

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Springer
V. Diekert , M.V. Volkov , M. Voronkov
Lecture Notes in Computer Science
Quantum Information Processing
International Symposium on Computer Science in Russia
Quantum Computing and Advanced System Research

Buhrman, H.M, Fortnow, L, Koucký, M, Rogers, J, & Vereshchagin, N.K. (2007). Inverting Onto Functions and Polynomial Hierarchy. In V Diekert, M.V Volkov, & M Voronkov (Eds.), Lecture Notes in Computer Science (pp. 92–103). Springer.