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Electronic Colloquium on Computational Complexity

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Reports tagged with upper bound:
TR94-011 | 12th December 1994
R. Beigel, W. Hurwood, N. Kahale

Fault Diagnosis in a Flash

We consider the fault diagnosis problem: how to use parallel testing
rounds to identify which processors in a set are faulty. We prove
that 4 rounds suffice when 3% or less of the processors are faulty,
and 4 rounds are necessary when any nontrivial constant fraction of
the processors are ... more >>>

TR07-054 | 25th May 2007
Shirley Halevy, Oded Lachish, Ilan Newman, Dekel Tsur

Testing Properties of Constraint-Graphs

We study a model of graph related formulae that we call
the \emph{Constraint-Graph model}. A
constraint-graph is a labeled multi-graph (a graph where loops
and parallel edges are allowed), where each edge $e$ is labeled
by a distinct Boolean variable and every vertex is
associate with a Boolean function over ... more >>>

TR11-094 | 20th June 2011
Shachar Lovett

Computing polynomials with few multiplications

A folklore result in arithmetic complexity shows that the number of multiplications required to compute some $n$-variate polynomial of degree $d$ is $\sqrt{{n+d \choose n}}$. We complement this by an almost matching upper bound, showing that any $n$-variate polynomial of degree $d$ over any field can be computed with only ... more >>>

TR15-173 | 29th October 2015
Martin Schwarz

An exponential time upper bound for Quantum Merlin-Arthur games with unentangled provers

We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless EXP=NEXP. The key ideas of our proof are to use perturbation theory to reduce ... more >>>

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