A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared sy...

Typical protocols for password-based authentication assume a single server which stores all the information (e.g., the password) necessary to authenticate a user. Unfortunately, an inherent limitation of this approach (assuming low-entropy passwords are used) is that the user’s password is exposed if this server is ever compromised. To address this issue, a number of schemes have been proposed ...

We consider irreducible 3–manifolds M that arise as knot complements in closed 3–manifolds and that contain at most two connected strict essential surfaces. The results in the paper relate the boundary slopes of the two surfaces to their genera and numbers of boundary components. Explicit quantitative relationships, with interesting asymptotic properties, are obtained in the case that M is a kn...

We consider the problem of orienting the edges of the n-dimensional hypercube so only two different in-degrees a and b occur. We show that this can be done, for two specified in-degrees, if and only if an obvious necessary condition holds. Namely, there exist non-negative integers s and t so that s + t = 2n and as + bt = n2. This is connected to a question arising from constructing a strategy f...

We study the problem of k-visibility in the memoryconstrained model. In this model, the input resides in a randomly accessible read-only memory of O(n) words with O(log n) bits each. An algorithm can read and write O(s) additional words of workspace during its execution, and it writes its output to write-only memory. In a given polygon P , for a given point q ∈ P , we say a point p is inside th...