## Speaker:

## Time:

## Venue:

- A-212 (STCS Seminar Room)

1. We show that every linear-invariant property that can be characterized by forbidding induced solutions to a (possibly infinite) set of linear equations can be tested with one-sided error.

2. We show that every linear-invariant property that can be tested with one-sided error can be characterized by forbidding induced solutions to a (possibly infinite) set of systems of linear equations.

We conjecture that our result from item (1) can be extended to cover systems of linear equations. We further show that the validity of this conjecture would have the following implications:

1. It would imply that every linear-invariant property that is closed under restrictions to linear subspaces is testable with one-sided error. Such a result would unify several previous results on testing Boolean functions, such as the results on testing low-degree

polynomials and results on testing Fourier dimensionality.

2. It would imply that a linear-invariant property P is testable with one-sided error *if and only if* P is closed under restrictions to linear subspaces, thus resolving Sudan's problem (joint work with Elena Grigorescu and Asaf Shapira).