Nondeterministic Extensions of the Strong Exponential Time Hypothesis and Consequences for Non-reducibility

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) fi ne-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 fi rst-order graph properties cannot be shown to be SETH-hard using deterministic or zero-error probabilistic reductions.