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We show that high dimensional expanders imply derandomized direct product tests, with a number of subsets that is linear in the size of the universe.Direct product tests belong to a family of tests called agreement tests that are important components in PCP constructions and include, for example, low degree tests such as line vs. line and plane vs. plane.For a generic hypergraph, we introduce the...
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The probability that the verifier accepts a false proof is called the soundness error, and is an important parameter of a PCP system that one seeks to minimize. Constructing...
The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set...
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