Research proof index

Chernoff lower bound

The cost of f >>= g is roughly f.cost + g.cost

query' costs one query, plus the rest

Completeness for any valid parameters

Alice wins the debate with good probability

A chain rule for conditional multidistance. Let $\pi:G\to H$ be a homomorphism, and suppose the pairs $(X_i,Y_i)$ are independent across the finite index set. Then $D[X\mid Y]=D[X\mid(\pi X,Y)]+D[\pi X\mid Y]+I\!\left[\sum_iX_i:(\pi X_i)_i\,\middle|\,\left(\pi\!\left(\sum_iX_i\right),(Y_i)_i\right)\right].$ The first term measures the remaining fiberwise multidistance after adjoining each image $\pi(X_i)$ to its conditioning data.