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Revision #1 to TR15-148 | 9th September 2015 22:51

Nondeterministic extensions of the Strong Exponential Time Hypothesis and consequences for non-reducibility

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Revision #1
Authors: Marco L. Carmosino, Jiawei Gao, Russell Impagliazzo, Ivan Mikhailin, Ramamohan Paturi, Stefan Schneider
Accepted on: 9th September 2015 22:52
Downloads: 802
Keywords: 


Abstract:

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.


Paper:

TR15-148 | 9th September 2015 00:49

Nondeterministic extensions of the Strong Exponential Time Hypothesis and consequences for non-reducibility


Abstract:

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.



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