Shin Aida, Rainer Schuler, Tatsuie Tsukiji, Osamu Watanabe

In this paper we separate many-one reducibility from truth-table

reducibility for distributional problems in DistNP under the

hypothesis that P neq NP. As a first example we consider the

3-Satisfiability problem (3SAT) with two different distributions

on 3CNF formulas. We show that 3SAT using a version of the

standard distribution ...
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Elmar Böhler, Christian Glaßer, Daniel Meister

SBP is a probabilistic promise class located

between MA and AM \cap BPPpath. The first

part of the paper studies the question of whether

SBP has many-one complete sets. We relate

this question to the existence of uniform

enumerations. We construct an oracle relative to

which SBP and AM do ...
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Elmar Böhler

A clone is a set of functions that is closed under generalized substitution.

The set FP of functions being computable deterministically in polynomial

time is such a clone. It is well-known that the set of subclones of every

clone forms a lattice. We study the lattice below FP, which ...
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Henning Wunderlich

In an unpublished Russian manuscript Razborov proved that a matrix family with high

rigidity over a finite field would yield a language outside the polynomial hierarchy

in communication complexity.

We present an alternative proof that strengthens the original result in several ways.

In particular, we replace rigidity by the strictly ...
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Vishnu Iyer, Siddhartha Jain, Matt Kovacs-Deak, Vinayak Kumar, Luke Schaeffer, Daochen Wang, Michael Whitmeyer

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions $f$, it is conjectured that $\mathrm{rdeg}(f)$ is polynomially related to $\mathrm{deg}(f)$, where $\mathrm{deg}(f)$ is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least $\mathrm{deg}(f)/2$ and ... more >>>