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.

, ,
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., 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.