Following Ergun et al. (JCSS 2000), we consider testing group properties and focus on the problem of testing whether a binary operation is a group operation.
That is, given a finite set $S$ and oracle access to a function $f:S\times S \to S$, we wish to distinguish the case that ... more >>>

We consider the problem of testing isomorphism to a fixed graph in the bounded-degree graph model. Our main result is that, for almost all $d$-regular $n$-vertex graphs $H$,
testing isomorphism to $H$ can be done using $\tildeO({\sqrt n})$ queries.
This result is shown to be optimal (up to ... more >>>

Considering the bounded-degree graph model, we show that if the degree bound is two,
then every graph property can be tested within query complexity that only depends on the proximity parameter.
Specifically, the query complexity is ${\rm poly}(1/\epsilon)$, where $\epsilon$ denotes the proximity parameter.
The key observation is that a ... more >>>