Testing problems with sub-learning sample complexity
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Exact and approximate testing/correcting of algebraic functions: a survey
Theoretical aspects of computer science
Proclaiming Dictators and Juntas or Testing Boolean Formulae
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Exact and Approximate Testing/Correcting of Algebraic Functions: A Survey
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
Breaking the ε-Soundness Bound of the Linearity Test over GF(2)
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Derandomizing graph tests for homomorphism
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On testing computability by small width OBDDs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
On the derandomization of the graph test for homomorphism over groups
Theoretical Computer Science
Short locally testable codes and proofs: a survey in two parts
Property testing
Introduction to testing graph properties
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Introduction to testing graph properties
Property testing
Short locally testable codes and proofs
Studies in complexity and cryptography
Introduction to testing graph properties
Studies in complexity and cryptography
Approximate judgement aggregation
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Approximately classic judgement aggregation
Annals of Mathematics and Artificial Intelligence
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Let Dist(f,g)=Pr/sub u/ [f(u)/spl ne/g(u)] denote the relative distance between functions f,g mapping from a group G to a group H, and let Dist(f) denote the minimum, over all linear functions (homomorphisms) g, of Dist(f,g). Given a function f:G/spl rarr/H we let Err(f)=Pr/sub u/,v[f(u)+f(v)/spl ne/f(u+v)] denote the rejection probability of the BLR (Blum-Luby-Rubinfeld) linearity test. Linearity testing is the study of the relationship between Err(f) and Dist(f), and in particular the study of lower bounds on Err(f) in terms of Dist(f). The case we are interested in is when the underlying groups are G=GF(2)/sup n/ and H=GF(2). The corresponding test is used in the construction of efficient PCPs and thence in the derivation of hardness of approximation results, and, in this context, improved analyses translate into better non-approximability results. However, while several analyses of the relation of Err(f) to Dist(f) are known, none is tight. We present a description of the relationship between Err(f) and Dist(f) which is nearly complete in all its aspects, and entirely complete (i.e. tight) in some. In particular we present functions L,U:[0,1]/spl rarr/[0,1] such that for all x/spl isin/[0,1] we have L(x)Err(f)/spl les/U(x) whenever Dist(f)=x, with the upper bound being tight on the whole range, and the lower bound tight on a large part of the range and close on the rest. Part of our strengthening is obtained by showing a new connection between the linearity testing problem and Fourier analysis, a connection which may be of independent interest. Our results are used by M. Bellare et al. (1995) to present the best known hardness results for Max3SAT and other MaxSNP problems.