Sunflowers and Testing Triangle-Freeness of Functions
نویسندگان
چکیده
منابع مشابه
On the Multiparty Communication Complexity of Testing Triangle-Freeness
In this paper we initiate the study of property testing in simultaneous and non-simultaneous multi-party communication complexity, focusing on testing triangle-freeness in graphs. We consider the coordinator model, where we have k players receiving private inputs, and a coordinator who receives no input; the coordinator can communicate with all the players, but the players cannot communicate wi...
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Understanding the query complexity for testing linear-invariant properties has been a central open problem in the study of algebraic property testing. Triangle-freeness in Boolean functions is a simple property whose testing complexity is unknown. Three Boolean functions f1, f2 and f3 : F2 → {0, 1} are said to be triangle free if there is no x, y ∈ F2 such that f1(x) = f2(y) = f3(x + y) = 1. Th...
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Call a function f : F 2 → {0, 1} odd-cycle-free if there are no x1, . . . , xk ∈ 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 ǫ-far from being odd-cycle-free by making poly(1/ǫ) queries to an evaluation oracle. To obtain this result, we use connections between basic Fourier analysis an...
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Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large d-dimensional...
متن کاملDistributedly Testing Cycle-Freeness
We tackle local distributed testing of graph properties. This framework is well suited to contexts in which data dispersed among the nodes of a network can be collected by some central authority (like in, e.g., sensor networks). In local distributed testing, each node can provide the central authority with just a few information about what it perceives from its neighboring environment, and, bas...
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ژورنال
عنوان ژورنال: computational complexity
سال: 2016
ISSN: 1016-3328,1420-8954
DOI: 10.1007/s00037-016-0138-7