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
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
A lower bound for testing juntas
Information Processing Letters
Journal of Computer and System Sciences - Special issue on FOCS 2002
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
Lower Bounds for Testing Function Isomorphism
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Testing Boolean function isomorphism
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Nearly tight bounds for testing function isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
IEEE Transactions on Information Theory
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A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is ''close'' to an isomorphism f"@s of f, we can compute f"@s(x) for anyx@?Z"2^n with good probability using q queries to g. We observe that any k-junta, that is, any function which depends only on k of its input variables, is O(2^k)-locally correctable. Moreover, we show that there are examples where this is essentially best possible, and locally correcting some k-juntas requires a number of queries which is exponential in k. These examples, however, are far from being typical, and indeed we prove that for almost every k-junta, O(klogk) queries suffice.