Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Three theorems regarding testing graph properties
Random Structures & Algorithms
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
Lower Bounds for Testing Bipartiteness in Dense Graphs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Generalizations of the removal lemma
Combinatorica
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A Unified Framework for Testing Linear-Invariant Properties
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Algorithmic Aspects of Property Testing in the Dense Graphs Model
SIAM Journal on Computing
IEEE Transactions on Information Theory
Hi-index | 0.00 |
A function f: Fn2 → {0, 1} is odd-cycle-free if there are no x1,..., xk ε Fn2 with k an odd integer such that f(x1) =... = f(xk) = 1 and x1 +... + xk = 0. We show that one can distinguish odd-cycle-free functions from those ε-far from being odd-cycle-free by making poly(1/ε) queries to an evaluation oracle. We give two proofs of this result, each shedding light on a different connection between testability of properties of Boolean functions and of dense graphs. The first problem we study is directly reducing testing linear-invariant properties of Boolean functions to testing associated graph properties. We show a black-box reduction from testing odd-cycle-freeness to testing bipartiteness of graphs. Such reductions have been shown previously (Král-Serra-Vena, Israel J. Math 2011; Shapira, STOC 2009) for monotone linear-invariant properties defined by forbidding solutions to a finite number of equations. But for odd-cycle-freeness whose description involves an infinite number of forbidden equations, a reduction to graph property testing was not previously known. If one could show such a reduction more generally for any linear-invariant property closed under restrictions to subspaces, then it would likely lead to a characterization of the one-sided testable linear-invariant properties, an open problem raised by Sudan. The second issue we study is whether there is an efficient canonical tester for linear-invariant properties of Boolean functions. A canonical tester for linear-invariant properties operates by picking a random linear subspace and then checking if the restriction of the input function to the subspace satisfies a fixed property or not. The question is whether for every linear-invariant property, there is a canonical tester for which there is only a polynomial blowup from the optimal query complexity. We answer the question affirmatively for odd-cycle-freeness. The general question still remains open.