2021/05/18 by Isolde Adler, Noleen Köhler, Adler, Isolde +3
Computer Science · #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #F.4.1 #FOS: Computer and information sciences #G.2.2 #Logic in Computer Science (cs.LO) #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2105.08490
openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Property Testing, proximity-oblivious testers (POTs) form a class of particularly simple testing algorithms, where a basic test is performed a number of times that may depend on the proximity parameter, but the basic test itself is independent of the proximity parameter. In their seminal work, Goldreich and Ron [STOC 2009; SICOMP 2011] show that the graph properties that allow constant-query proximity-oblivious testing in the bounded-degree model are precisely the properties that can be expressed as a generalised subgraph freeness (GSF) property that satisfies the non-propagation condition. It is left open whether the non-propagation condition is necessary. Indeed, calling properties expressible as a generalised subgraph freeness property GSF-local properties, they ask whether all GSF-local properties are non-propagating. We give a negative answer by exhibiting a property of graphs that is GSF-local and propagating. Hence in particular, our property does not admit a POT, despite being GSF-local. We prove our result by exploiting a recent work of the authors which constructed a first-order (FO) property that is not testable [SODA 2021], and a new connection between FO properties and GSF-local properties via neighbourhood profiles.