The subcubic (O(n) for ω < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = AB but if Cij = 1 they do not find an index k (a witness) such that Aik = Bkj = 1. We design a deterministic algorithm for computing the matrix of witnesses that runs in Õ(n) time, where here Õ(n) denotes O(n(log n)). The subcubic methods to compute the shortest distances...

Eyewitnesses sometimes view more than one lineup during an investigation. We investigated the effects of postidentification feedback following one lineup on responses to a second lineup. Witnesses (N=621) viewed a mock crime and, later, attempted to identify the culprit from an initial (target-absent) lineup and a second (target-present or target-absent) lineup. Prior to viewing the second line...

testimony is one of the most important reasons that legislator has accounted for proving the litigation and it is of special importance. witness is the most important pillar of testimony. due to great and special influence of testimony to prove or disprove the litigations, it is necessary to qualify the witness. one of the most important qualifications of the witness is his justice. justice is ...

A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the entanglement detection of any N-partite quantum system. For this purpose, a map from convex space of separable density matrices to a convex region called feasible ...

If a is not a multiple of « and a"~ ' * 1 mod n, then n must be composite and a is called a "witness" for «. Let F(n) denote the number of "false witnesses" for n, that is, the number of a mod n with a"-1 s l mod «. Considered here is the normal and average size of F( « ) for « composite. Also considered is the situation for the more stringent Euler and strong pseudoprime tests.

We present a possible computational content of the negative translation of classical analysis with the Axiom of Choice Our interpretation seems computationally more direct than the one based on G odel s Dialectica interpretation Interestingly this interpretation uses a re nement of the realizibility semantics of the absurdity proposition which is not interpreted as the empty type here We also s...

The category of effect algebras is the Eilenberg-Moore category for the monad arising from the free-forgetful adjunction between categories of bounded posets and orthomodular posets. In the category of effect algebras, an observable is a morphism whose domain is a Boolean algebra. The characterization of subsets of ranges of observables is an open problem. For an interval effect algebra E, a wi...

An observableW that distinguishes all the unentangled states from some entangled states is called a witness. We consider witnesses on n qbits, and use the following normalization: A witness W satisfies |tr(Wρ)| ≤ 1 for all separable states ρ, while kWk > 1, with the norm being the maximum among the absolute values of the eigenvalues of W . Although there are n-qbit witnesses whose norm is expon...