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Does the Polynomial Hierarchy Collapse if Onto Functions are Invertible?
2008
Theory of Computing Systems
The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomial-time does this imply the polynomial-time hierarchy collapses? By computing a multivalued function in deterministic polynomial-time we mean on every input producing one of the possible values of the function on that input. We give a
doi:10.1007/s00224-008-9160-8
fatcat:pxvzqb3xnvemjcipo54baee7ky