Separations of Matroid Freeness Properties

Properties of Boolean functions on the hypercube that are invariant with respect to linear transformations of the domain are among some of the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of linear-invariant properties called matroid freeness properties. These properties have been conjectured to essentially coincide with all testable linear-invariant properties, and a recent sequence of works has established testability for increasingly larger subclasses of matroid freeness properties. One question that has been left open, however, is whether the infinitely many syntactically different matroid freeness properties recently shown to be testable in fact correspond to new, semantically distinct properties. This is a crucial issue since it has also been shown previously that there exist subclasses of matroid freeness properties for which an infinite set of syntactically different representations collapse into one of a small,...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordström, Ning Xie
• Keywords: CORR 2010, Education, Freeness Properties, Linear-invariant Properties, Matroid Freeness Properties