What is a Knowledge State?

• X = all configurations (pairs of points), itself a metric space under the minimum matching metric.

• A knowledge state k = (ω,π) where:

• ω: X → R is the estimator

• π is a distribution on X

• If {x,y} ∈ X, then

  • π(x,y) is the probability we are at {x,y}.

  • ω(x,y) is the estimated unpaid cost of the adversary if it is at{x,y}.

• A knowledge state also has a potential, φ(k).