All Superlinear Inverse Schemes are coNP-Hard

TL;DR

This paper proves that inverting NP problems with superlinear certificates is coNP-hard, introducing a new proof technique that constructs diagonalizations within circuits to establish this complexity result.

Contribution

It establishes the coNP-hardness of all superlinear inverse schemes for NP problems using a novel diagonalization-based proof technique.

Findings

Superlinear inverse schemes are coNP-hard.

Introduces a new proof technique involving diagonalizations in circuits.

Provides a complexity classification for inverse problems of NP.

Abstract

How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.