Consequences of APSP, triangle detection, and 3SUM hardness for separation between determinism and non-determinism

TL;DR

This paper explores how well-known computational conjectures like APSP, 3SUM, and ETH influence the separation between deterministic and non-deterministic complexity classes, highlighting their implications and dependencies on input parameters.

Contribution

It provides a formal framework connecting these conjectures to class separations, emphasizing the role of input range parameters in these relationships.

Findings

Implications of APSP, 3SUM, and ETH conjectures on class separations

Different dependencies on input range parameters for each conjecture

Formalization of negated containment relations involving non-deterministic oracles

Abstract

We present implications from the known conjectures like APSP, 3SUM and ETH in a form of a negated containment of a linear-time with a non-deterministic logarithmic-bit oracle in a respective deterministic bounded-time class They are different for different conjectures and they exhibit in particular the dependency on the input range parameters.