Toda's theorem

Toda's theorem

The Toda's Theorem was proven by Seinosuke Toda in his paper "PP is as Hard as the Polynomial-Time Hierarchy" (1991) and was given 1998 Gödel Prize. The theorem considers solution-counting for polynomial problem class PP and polynomial hierarchy PH and states that latter notion subsumes the former - for any problem in the polynomial hierarchy there is a deterministic polynomial time reduction to counting. [ [http://sigact.acm.org/prizes/godel/1998.html 1998 Gödel Prize. Seinosuke Toda] ]

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