We introduce the Nondeterministic Strong Exponential Time Hypothesis
(NSETH) as a natural extension of the Strong Exponential Time
Hypothesis (SETH). We show that both refuting and proving
NSETH would have interesting consequences.

In particular we show that disproving NSETH would give new
nontrivial circuit lower bounds. On the other hand, NSETH
implies non-reducibility results, i.e. the absence of
(deterministic) fine-grained reductions from SAT to a
number of problems. As a consequence we conclude that unless
this hypothesis fails, problems such as 3-Sum, APSP
and model checking of a large class of first-order graph properties
cannot be shown to be SETH-hard using deterministic or
zero-error probabilistic reductions.

We introduce the Nondeterministic Strong Exponential Time Hypothesis
(NSETH) as a natural extension of the Strong Exponential Time
Hypothesis (SETH). We show that both refuting and proving
NSETH would have interesting consequences.

In particular we show that disproving NSETH would give new
nontrivial circuit lower bounds. On the other hand, NSETH
implies non-reducibility results, i.e. the absence of
(deterministic) fine-grained reductions from SAT to a
number of problems. As a consequence we conclude that unless
this hypothesis fails, problems such as 3-Sum, APSP
and model checking of a large class of first-order graph properties
cannot be shown to be SETH-hard using deterministic or
zero-error probabilistic reductions.