Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A function  f  : Fn/2 → {0,1} is triangle-free if there are no  x  1 ,  x  2 ,  x  3  ∈ Fn/2 satisfying  x  1  +  x  2  +  x  3  --0 and  f ( x  1 ) --  f ( x  2 ) --  f ( x  3 ) -- 1. In testing triangle freeness, the goal is to distinguish with high probability triangle-free functions from those which are e-far from being triangle-free. It was shown by Green that the query complexity of the canonical tester for the problem is upper bounded by a function that depends only on e (GAFA, 2005), hover the best known upper bound is a tor type function of 1/e. The best known lor bound on the query complexity of the canonical tester is 1/e 13.239  (Fu and Kleinberg, RANDOM, 2014).   In this work  introduce a new approach to proving lor bounds on the query complexity of triangle-freeness.  relate the problem to combinatorial questions on collections of vectors in Zn/D and to sunflor conjectures studied by Alon, Shpilka, and Umans (Comput. Complex., 2013). The relations yield that a refutation of the ak Sunflor Conjecture over Z 4  implies a super-polynomial lor bound on the query complexity of the canonical tester for triangle-freeness. Our results are extended to testing  k -cycle-freeness of functions with domain F n/p  for every  k  > 3 and a prime  p . In addition,  generalize the lor bound of Fu and Kleinberg to  k -cycle-freeness for  k  > 4 by generalizing the construction of uniquely solvable puzzles due to Coppersmith and Winograd (J. Symbolic Comput., 1990).
['Ishay Haviv', 'Ning Xie']
I am writing a research paper on a idea Sunflowers and Testing Triangle-Freeness of Functions
[{"from": "human", "value": "I am writing a research paper on a idea Sunflowers and Testing Triangle-Freeness of Functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A function  f  : Fn/2 \u2192 {0,1} is triangle-free if there are no  x  1 ,  x  2 ,  x  3  \u2208 Fn/2 satisfying  x  1  +  x  2  +  x  3  --0 and  f ( x  1 ) --  f ( x  2 ) --  f ( x  3 ) -- 1. In testing triangle freeness, the goal is to distinguish with high probability triangle-free functions from those which are e-far from being triangle-free. It was shown by Green that the query complexity of the canonical tester for the problem is upper bounded by a function that depends only on e (GAFA, 2005), hover the best known upper bound is a tor type function of 1/e. The best known lor bound on the query complexity of the canonical tester is 1/e 13.239  (Fu and Kleinberg, RANDOM, 2014).   In this work  introduce a new approach to proving lor bounds on the query complexity of triangle-freeness.  relate the problem to combinatorial questions on collections of vectors in Zn/D and to sunflor conjectures studied by Alon, Shpilka, and Umans (Comput. Complex., 2013). The relations yield that a refutation of the ak Sunflor Conjecture over Z 4  implies a super-polynomial lor bound on the query complexity of the canonical tester for triangle-freeness. Our results are extended to testing  k -cycle-freeness of functions with domain F n/p  for every  k  > 3 and a prime  p . In addition,  generalize the lor bound of Fu and Kleinberg to  k -cycle-freeness for  k  > 4 by generalizing the construction of uniquely solvable puzzles due to Coppersmith and Winograd (J. Symbolic Comput., 1990)."}]