| import OAI.Probability.MatroidProphet.Main |
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|
| namespace OAI |
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|
| namespace MatroidProphet |
| open Set Finset MeasureTheory |
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| / |
| observations, complete accepted-set nonanticipation, irrevocability, and literal |
| rejection of sacrificed labels. The mask depends only on the initial seed by |
| the type of `HiddenRule`; no weight-dependent mask is allowed. -/ |
| def MainRuleFeasibility {n bits : ℕ} (M : Matroid (Fin n)) |
| (A : HiddenRule n bits) : Prop := |
| Feasible M A.core ∧ |
| (∀ k, Measurable (fun x : Seed bits × (Weights n × History n k) => |
| A.core.decide k x.1 (observed A x.1 x.2.1) x.2.2)) ∧ |
| (∀ (w : Weights n), (∀ e, 0 ≤ w e) → |
| ∀ (r : Seed bits) (π : ArrivalOrder n) (t : ℕ), |
| M.Indep (hiddenAcceptedThrough A r w π t : Set (Fin n))) ∧ |
| (∀ (r : Seed bits) (w w' : Weights n) (π π' : ArrivalOrder n) (t : ℕ), |
| (∀ e ∈ A.mask r, w e = w' e) → |
| (∀ j : Fin n, j.val < t → (π j, w (π j)) = (π' j, w' (π' j))) → |
| hiddenAcceptedThrough A r w π t = hiddenAcceptedThrough A r w' π' t) ∧ |
| (∀ (r : Seed bits) (w : Weights n) (π : ArrivalOrder n), |
| Monotone (hiddenAcceptedThrough A r w π)) ∧ |
| (∀ (r : Seed bits) (w : Weights n) (π : ArrivalOrder n) (t : ℕ), |
| Disjoint (hiddenAcceptedThrough A r w π t) (A.mask r)) |
|
|
| end MatroidProphet |
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| end OAI |
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|
