High Quality Content by WIKIPEDIA articles! In Boolean algebra, a parity function is a Boolean function whose value is 1 if the input vector has odd number of ones. The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions. In early 1980s Merrick Furst, James Saxe and Michael Sipser and independently Miklos Ajtai established super-polynomial lower bounds on the size of constant-depth Boolean circuits for the parity function,i.e., they have shown that polynomial-size constant-depth circuits cannot compute the parity function. Similar results were also established for the majority, multiplication and transitive closure functions, by reduction to the parity function problem. Until this time only linear lower bounds were known for various naturally arising functions.

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