Definition 1 Sample Clauses

Definition 1. Given a (hash) function H, we play the following game. An adversary A generates a quantum state |φ) = x X αx |x) such that H(x) = c for all x ∈ X for some c. Then, one of the following happens:

Definition 1. (Action). An action is a tuple consisting of three elements p, an, d , where p is the principal, an is an action name, and d is the data.

Definition 1. Suppose we are given an optimization problem defined by a cost function R(c, X) R, where c is a solution from the finite solution space and X is a random data instance. Then the Xxxxx posterior distribution pβ(c|X) is defined as Σ| − − p (c X) = 1 exp( βR(c, X)) with Z(β, X) = exp( βR(cj, X)) . β Z(β, X) ct∈C

Definition 1. 3.1. A unital C∗-algebra is called a C∗-algebra of real rank zero if any its self-adjoint element can be approximated by elements with finite spectra.