The complexity class PP
Lax666725.UnboundedError · concepts/Lax666725/UnboundedError.lean · lax-666725
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Definition
A binary language belongs to if a polynomial-time probabilistic machine answers correctly with probability strictly greater than on every input. No constant or inverse-polynomial lower bound on the advantage over is imposed. We use the strict-correctness convention on both members and nonmembers; ties do not count as success.
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| 1 | import Lax666725.ProbabilisticMachines |
| 2 | |
| 3 | /-! |
| 4 | --- |
| 5 | title: The complexity class PP |
| 6 | type: definition |
| 7 | --- |
| 8 | A binary language belongs to if a polynomial-time |
| 9 | probabilistic machine answers correctly with probability strictly greater |
| 10 | than on every input. No constant or inverse-polynomial lower bound |
| 11 | on the advantage over is imposed. We use the strict-correctness |
| 12 | convention on both members and nonmembers; ties do not count as success. |
| 13 | -/ |
| 14 | |
| 15 | namespace Lax666725.UnboundedError |
| 16 | |
| 17 | open Lax434930.PolynomialTime ProbabilisticMachines |
| 18 | |
| 19 | def PP : Set Language := |
| 20 | {L | ∃ A : Procedure Bool, ∀ x, (1 / 2 : ℚ) < A.probability x (Correct L x)} |
| 21 | |
| 22 | end Lax666725.UnboundedError |
| 23 |
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