The local order in a supercooled monodisperse colloidal fluid is studied by direct imaging of the particles with a laser scanning confocal microscope. The local structure is analysed with a bond order parameter method, which allows one to discern simple structures that are relevant in this system. As expected for samples that crystallize eventually, a large fraction of the particles are found t...

We introduce PEP, the Post Embedding Problem, a variant of PCP where one compares strings with the subword relation, and PEPreg, a further variant where solutions are constrained and must belong to a given regular language. PEPreg is decidable but not primitive recursive. This entails the decidability of reachability for unidirectional systems with one reliable and one lossy channel.

In a recent paper, Savas, Batta and Nagi [14] consider the optimal placement of a finite-sized facility in the presence of arbitrarily-shaped barriers under rectilinear travel. Their model applies to a layout context, since barriers can be thought to be existing departments and the finite-sized facility can be viewed as the new department to be placed. In a layout situation, the existing and ne...

For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if the ratio of the number of elements of length n+ 1 over the number of elements of length n of the language h...

This paper addresses the problem of inferring a regular expression from a given set of strings that resembles, as closely as possible, the regular expression that a human expert would have written to identify the language. This is motivated by our goal of automating the task of postmasters of an email service who use regular expressions to describe and blacklist email spam campaigns. Training d...

We establish universality limits for measures on a smooth closed contour Γ in the plane. Assume that μ is a regular measure on Γ, in the sense of Stahl, Totik, and Ullmann. Let Γ1 be a closed subarc of Γ, such that μ is absolutely continuous in an open arc containing Γ1, and μ′ is positive and continuous in that open subarc. Then universality for μ holds in Γ1, in the sense that the reproducing...

In a radar imaging problem using broad-band, low-frequency waves, we encounter the problem of solving Poisson's equation over a very large rectangular grid, typically ve thousand times thousand pixels. In addition, no information about boundary values is available. In order to select suitable solutions we solve the Poisson equation under the side condition that some criterion function, usually ...

Simion has a conjecture concerning the number of lattice paths in a rectangular grid with the Ferrer's diagram of a partition removed. The conjecture concerns the unimodality of this number over a sequence of rectangles with the sum of the length and width being constant and with a constant partition. This paper demonstrates this unimodality if the partition is symmetric or if the Ferrer's diag...

In [7], a new version of Brzozowski’s algorithm was put forward which relies on regular expression hashing to possibly decrease the number of states in the generated finite state automata. This method utilizes a hash function to decide which states are merged, but does not, in general, construct *-equivalence classes on automaton states, as is done in minimization algorithms. The consequences o...

We describe three regular expression-based methods to characterize as a regular language the language defined by a two-way automaton. The construction methods yield relatively simple techniques to directly construct one-way automata that simulate the behavior of two-way automata. The approaches also offer conceptually uncomplicated alternative equivalence proofs of two-way automata and one-way ...