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

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.