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- W2398887852 abstract "Unambiguous hierarchies 1-3] are defined similarly to the polynomial hierarchy; however, all witnesses must be unique. These hierarchies have subtle differences in the mode of using oracles. We consider a loose unambiguous hierarchy pr UH with relaxed definition of oracle access to promise problems. Namely, we allow to make queries that miss the promise set; however, the oracle answer in this case can be arbitrary (a similar definition of oracle access has been used in 4]).In this short note we prove that the first part of Toda's theorem PH ? BP ? ? P ? P PP can be strengthened to PH = BP ? pr UH , that is, the closure of our hierarchy under Schoning's BP operator equals the polynomial hierarchy. It is easily seen that BP ? pr UH ? BP ? ? P .The proof follows the same lines as Toda's proof, so the main contribution of the present note is a new definition that allows to characterize PH as a probabilistic closure of unambiguous computations. We introduce a new version prUH of the unambiguous hierarchy of promise problems.We prove that PH = BP ? prUH .Our result strengthens the first part of Toda's theorem PH ? BP ? ? P ? P PP , as BP ? prUH ? BP ? ? P ." @default.
- W2398887852 created "2016-06-24" @default.
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- W2398887852 date "2014-01-01" @default.
- W2398887852 modified "2023-09-23" @default.
- W2398887852 title "On the probabilistic closure of the loose unambiguous hierarchy." @default.
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