Revision #2 Authors: Oded Goldreich, Guy Rothblum

Accepted on: 22nd January 2018 17:38

Downloads: 41

Keywords:

For every polynomial $q$, we present worst-case to average-case (almost-linear-time) reductions for a class of problems in $\cal P$ that are widely conjectured not to be solvable in time $q$.

These classes contain, for example, the problems of counting the number of $k$-cliques in a graph, for any fixed $k\geq3$.

In general, we consider the class of problems that consist of counting the number of local neighborhoods in the input that satisfy some predetermined conditions, where the number

of neighborhoods is polynomial, and the neighborhoods as well as the conditions can be specified by small uniform Boolean formulas.

Hence, we show an almost-linear-time reduction from solving one such problem in the worst-case to solving some other problem (in the same class) on typical inputs.

minor revision

Revision #1 Authors: Oded Goldreich, Guy Rothblum

Accepted on: 21st January 2018 16:03

Downloads: 35

Keywords:

For every polynomial $q$, we present worst-case to average-case (almost-linear-time) reductions for a class of problems in $\cal P$ that are widely conjectured not to be solvable in time $q$.

These classes contain, for example, the problems of counting the number of $k$-cliques in a graph, for any fixed $k\geq3$.

In general, we consider the class of problems that consist of counting the number of local neighborhoods in the input that satisfy some predetermined conditions, where the number

of neighborhoods is polynomial, and the neighborhoods as well as the conditions can be specified by small uniform Boolean formulas.

Hence, we show an almost-linear-time reduction from solving one such problem in the worst-case to solving some other problem (in the same class) on typical inputs.

Added an overview of the techniques (Sec 1.3),

and a comment on worst-case to average-case reductions for a uniform version of AC0[2].

TR17-130 Authors: Oded Goldreich, Guy Rothblum

Publication: 30th August 2017 11:42

Downloads: 564

Keywords:

For every polynomial $q$, we present worst-case to average-case (almost-linear-time) reductions for a class of problems in $\cal P$ that are widely conjectured not to be solvable in time $q$.

These classes contain, for example, the problems of counting the number of $k$-cliques in a graph, for any fixed $k\geq3$.

In general, we consider the class of problems that consist of counting the number of local neighborhoods in the input that satisfy some predetermined conditions, where the number

of neighborhoods is polynomial, and the neighborhoods as well as the conditions can be specified by small uniform Boolean formulas.

Hence, we show an almost-linear-time reduction from solving one such problem in the worst-case to solving some other problem (in the same class) on typical inputs.