Weboptimal testing reed-muller code degree polynomial gowers norm 1-query test tight relationship rejection probability alon et optimal analysis reed-muller testing problem st-gowers norm WebWe consider the problem of testing if a given function $f : \\F_2^n \\right arrow \\F_2$ is close to any degree $d$ polynomial in $n$ variables, also known as the ...

Optimal Testing of Reed-Muller Code Property testing

WebOct 4, 2009 · Alon et al. [AKK+05] proposed and analyzed a natural 2d + 1-query test T 0, and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are Ω (1)-far... WebThis leads to a O(d4 d)-query test for degree d Reed-Muller codes. We give an asymptotically optimal analysis of T 0, showing that it rejects functions that are ω(1)-far with ω(1)-probability (so the rejection probability is a universal constant independent of d and n). In particular, this implies that the query complexity of testing degree d ... church\\u0027s jalapeno cheese bombers recipe

Lecture 21: Reed-Muller Codes - University at Buffalo

Webcally) testing Reed-Muller codes. Their strategy is then to pick a random minimum-weight codeword from the dual code and to check if it is orthogonal to the tested vector. It is important to note that these minimum-weight code words generate the Reed-Muller code. Specifically their test works as follows: given a function f : f0;1gn! f0;1g, to ... WebOptimal Testing of Reed-Muller Codes Abstract: We consider the problem of testing if a given function f:F 2 n → F 2 is close to any degree d polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al. [1] proposed and analyzed a natural 2 d+1 -query test for this problem. WebAlon et al. [AKK+05] proposed and analyzed a natural 2 d+1-query test T 0, and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are … dfa passport schedule 2022