TY - GEN
T1 - Proximity oblivious testing and the role of invariances
AU - Goldreich, Oded
AU - Kaufman, Tali
PY - 2011
Y1 - 2011
N2 - We present a general notion of properties that are characterized by local conditions that are invariant under a sufficiently rich class of symmetries. Our framework generalizes two popular models of testing graph properties as well as the algebraic invariances studied by Kaufman and Sudan (STOC'08). Our focus is on the case that the property is characterized by a constant number of local conditions and a rich set of invariances. We show that, in the aforementioned models of testing graph properties, characterization by such invariant local conditions is closely related to proximity oblivious testing (as defined by Goldreich and Ron, STOC'09). In contrast to this relation, we show that, in general, characterization by invariant local conditions is neither necessary nor sufficient for proximity oblivious testing. Furthermore, we show that easy testability is not guaranteed even when the property is characterized by local conditions that are invariant under a 1-transitive group of permutations.
AB - We present a general notion of properties that are characterized by local conditions that are invariant under a sufficiently rich class of symmetries. Our framework generalizes two popular models of testing graph properties as well as the algebraic invariances studied by Kaufman and Sudan (STOC'08). Our focus is on the case that the property is characterized by a constant number of local conditions and a rich set of invariances. We show that, in the aforementioned models of testing graph properties, characterization by such invariant local conditions is closely related to proximity oblivious testing (as defined by Goldreich and Ron, STOC'09). In contrast to this relation, we show that, in general, characterization by invariant local conditions is neither necessary nor sufficient for proximity oblivious testing. Furthermore, we show that easy testability is not guaranteed even when the property is characterized by local conditions that are invariant under a 1-transitive group of permutations.
KW - Graph Properties
KW - Locally Testable Codes
KW - Property Testing
KW - Sparse Linear Codes
KW - The Long-Code
UR - https://www.scopus.com/pages/publications/80052362378
U2 - 10.1007/978-3-642-22935-0_49
DO - 10.1007/978-3-642-22935-0_49
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AN - SCOPUS:80052362378
SN - 9783642229343
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 579
EP - 582
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Y2 - 17 August 2011 through 19 August 2011
ER -