Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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The Investigation of Chow parameters is extended to pseudothreshold functions. Pseudothreshold logic is a generalization of threshold logic. Chow parameters are a set of n + 1 integers derived from a Boolean function of n variables. The main results are: 1. Two different pseudothreshold functions with the same Chow parameters have the same optimum structure. Thus, the optimum structures of pseudothreshold functions can be cataloged using Chow parameters. 2. The set of positive threshold functions is a subset of the set of positive, zero-free, pseudothreshold functions which is a subset of the nonnegative, nontrivial pseudothreshold functions which in turn is a subset of the measure minimum functions. 3. The set of positive threshold functions is a subset of the Intersection of the set of positive Chow unique functions and positive, zero-free, pseudothreshold functions. 4. The sets of positive Chow unique functions and the positive, zero-free, pseudothreshold functions are subsets of the Chow maximum functions which in turn is a subset of the positive Boolean functions.