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PP is closed under intersection
Abstract: "In his seminal paper on probabilistic Turing machines, Gill [Gil77] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. In fact, PP is closed under polynomial-time multilinear reductions. In circuits, this allows us to combine several threshold gates into a single threshold gate, while increasing depth by only a constant. Consequences in complexity theory include definite collapse and plausible separation of certain query hierarchies over PP.
- "Abstract: "In his seminal paper on probabilistic Turing machines, Gill [Gil77] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. In fact, PP is closed under polynomial-time multilinear reductions. In circuits, this allows us to combine several threshold gates into a single threshold gate, while increasing depth by only a constant. Consequences in complexity theory include definite collapse and plausible separation of certain query hierarchies over PP."@en
- "Consequences in the study of circuits include the simulation of circuits with a small number of threshold gates by circuits having only a single threshold gate at the root (perceptrons), and a lower bound on the number of threshold gates needed in order to compute the parity function.""@en
- "PP is closed under intersection"
- "PP is closed under intersection"@en