TL;DR
This paper introduces a new concept called list agreement expansion, providing conditions for set systems to exhibit this property and connecting it to coboundary expansion and direct sum testing, advancing agreement testing theory.
Contribution
It is the first work to explore list agreement expansion, establishing sufficient conditions and linking it to coboundary expansion and direct sum testing techniques.
Findings
List agreement expansion requires different techniques than agreement expansion.
Set systems with list agreement expansion support direct sum testing.
The work connects covering spaces of complexes with coboundaries for testing structures.
Abstract
One of the key components in PCP constructions are agreement tests. In agreement test the tester is given access to subsets of fixed size of some set, each equipped with an assignment. The tester is then tasked with testing whether these local assignments agree with some global assignment over the entire set. One natural generalization of this concept is the case where, instead of a single assignment to each local view, the tester is given access to different assignments for every subset. The tester is then tasked with testing whether there exist global functions that agree with all of the assignments of all of the local views. In this work we present sufficient condition for a set system to exhibit this generalized definition of list agreement expansion. This is, to our knowledge, the first work to consider this natural generalization of agreement testing. Despite initially…
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Videos
List Agreement Expansion from Coboundary Expansion· youtube
