Given a disk O in the plane called the objective, we want to find n small disks P1, . . . , Pn called the pupils such that ⋃n i,j=1 Pi ⊖ Pj ⊇ O, where ⊖ denotes the Minkowski difference operator, while minimizing the number of pupils, the sum of the radii or the total area of the pupils. This problem is motivated by the construction of very large telescopes from several smaller ones by so-calle...

We consider here a variation of Vector Addition Systems where one counter can be tested for zero. We extend the reachability proof for Vector Addition System recently published by Leroux to this model. This provides an alternate, more conceptual proof of the reachability problem that was originally proved by Reinhardt.

We consider the problem of listing faces of the Minkowski sum of several V-polytopes in R. An algorithm for listing all faces of dimension up to j is presented, for any given 0 ≤ j ≤ d − 1. It runs in time polynomial in the sizes of input and output.

AAA 2

We consider the problem of traveling the contour of the set of all points that are within distance 1 of a connected planar curve arrangement P, forming an embedding of the graph G. We show that if the overall length of P is L, there is a closed roundtrip that visits all points of the contour and has length no longer than 2L + 2. This result carries over in a more general setting: if R is a comp...

In this paper, results from a perception experiment on perceived prosodic boundary strength in spontaneous speech are presented. The analysis of the listeners’ responses reveals a good agreement in rating the strength of prosodic phrase boundaries on a visual analogue scale (VAS), and a strong correlation between perceived boundary strength and pause duration.

This paper makes three original contributions: (1) Explicit closed-form parametric formulas for the boundary of the Minkowski sum and difference of two arbitrarily oriented solid ellipsoids in n-dimensional Euclidean space are presented; (2) Based on this, new closed-form lower and upper bounds for the volume contained in these Minkowski sums and differences are derived in the 2D and 3D cases a...

We investigate a lattice construction method for the Coppersmith technique for finding small solutions of a modular equation. We consider its variant for simultaneous equations and propose a method to construct a lattice by combining lattices for solving single equations. As applications, we consider a new RSA cryptanalyses. Our algorithm can factor an RSA modulus from l ≥ 2 pairs of RSA public...

The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes called perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of faces of the sum in terms of the face lattice of a given perfectly centered polytope. Exact face coun...