## One-Sided Error Testing of Monomials and Affine Subspaces

#### Webpage for a paper by Oded Goldreich amd Dana Ron

#### Abstract

We consider the query complexity of three versions of the problem
of testing monomials and affine (and linear) subspaces
with one-sided error, and obtain the following results:

- The general problem, in which the arity of the monomial
(resp., co-dimension of the subspace) is not specified,
has query complexity ${\widetilde{O}}(1/\epsilon)$,
where $\epsilon$ denotes the proximity parameter.
- The bounded problem, in which the arity of the monomial
(resp., co-dimension of the subspace)
is upper bounded by a fixed parameter,
has query complexity ${\widetilde{O}}(1/\epsilon)$,
- The exact problem, in which the arity of the monomial
(resp., co-dimension of the subspace) is required to equal
a fixed parameter (e.g., equals~2),
has query complexity ${\widetilde{\Omega}}(\log n)$,
where $n$ denotes the length of the argument for the tested function.

The running time of the testers in the positive results
is linear in their query complexity.

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