Abstract
We consider the problem of determining whether a given function f: {0, 1n} → {0, 1} belongs to a certain class of Boolean functions \( \mathcal{F} \) or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ε, we would like to decide whether f ∈ \( \mathcal{F} \) or whether it differs from every g ∈ \( \mathcal{F} \) on more than an ε-fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.
Supported by the Israel Science Foundation (grant number 32/00-1).
Supported by the NSF (grant number CCR-9987845)
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Parnas, M., Ron, D., Samorodnitsky, A. (2001). Proclaiming Dictators and Juntas or Testing Boolean Formulae. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_30
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DOI: https://doi.org/10.1007/3-540-44666-4_30
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