Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.probabilistic-reachability

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/probabilistic_reachability.clj1 definitions, 4 theorems

AHoF V51 Probabilistic Reachability: compute the probability of reaching a target set and flag it likely-reachable when that probability meets a confidence threshold: likely-reachable? probability threshold = decide (threshold <= probability). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.probabilistic-reachability` prints this classification.

prob-reach/likely-reachable? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

prob-reach/high-probability-likely :
  → bo/is-safe 3/4 1/2 = data/true

prob-reach/boundary-likely :
  → bo/is-safe 1/2 1/2 = data/true

prob-reach/probability-certificate :
  → 1/2 ≤ 3/4

prob-reach/low-probability-unlikely :
  → bo/is-safe 1/4 1/2 = data/false