$K$-Continuity Is Equivalent To $K$-Exactness

Pentacam equivalent K-reading.

Constraint Problems: Computability Is Equivalent to Continuity

In many practical situations, we would like to compute the set of all possible values that satisfy given constraints. It is known that even for computable (constructive) constraints, computing such set is not always algorithmically possible. One reason for this algorithmic impossibility is that sometimes, the dependence of the desired set on the parameters of the problem is not continuous, whil...

CHROMATICALLY EQUIVALENT k-BRIDGE HYPERGRAPHS

An h-uniform hypergraph (h ≥ 2) H = (V, E) of order n = |V| and size m = |E|, consists of a vertex set V(H) = V and edge set E(H) = E , where E ⊂ V and |E| = h for each edge E in E . H is said to be linear if 0 ≤ |E ∩ F | ≤ 1 for any two distinct edges E,F ∈ E(H) [1]. Let P h,1 p denote the linear path consisting of p ≥ 1 edges E1, . . . , Ep such that |E1| = . . . = |Ep| = h, |Ek ∩ El| = 1 if ...

C K Continuity of Subdivision Surfaces

Stationary subdivision is an important tool for generating smooth free-form surfaces for CAGD and computer graphics. One of the challenges in construction of subdivision schemes for arbitrary meshes is to guarantee that the limit surface will have smooth regular parameterization in a neighborhood of any point. First results in this direction were obtained only recently. In this paper we derive ...

Boneh et al.'s k-Element Aggregate Extraction Assumption Is Equivalent to the Diffie-Hellman Assumption

In Eurocrypt 2003, Boneh et al. presented a novel cryptographic primitive called aggregate signatures. An aggregate signature scheme is a digital signature that supports aggregation: i.e. given k signatures on k distinct messages from k different users it is possible to aggregate all these signatures into a single short signature. Applying the above concept to verifiably encrypted signatures, B...