A zonotope is the Minkowski addition of line segments in Rd. The zonotope construction problem is to list all extreme points of a zonotope given by its line segments. By duality, it is equivalent to the arrangement construction problem that is to generate all regions of an arrangement of hyperplanes. By replacing line segments with convex V-polytopes, we obtain a natural generalization of the z...

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that a...

The paper discusses the problem of determinising finite-state automata containing large numbers of e-moves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very large number of emoves. The paper identifies three subset construction algorithms which treat e-moves. A number of experiments has been performed which indicate tha...

Using the concept of progress measure, we give a new proof of Rabin’s fundamental result that the languages defined by tree automata are closed under complementation. To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition. Immediate determinancy is stronger t...

The problem of “evenly” distributing points on a sphere has a long history. Albeit its intuitive meaning, it is necessary to define “even distribution” mathematically. Various metrics, θs, 0 ≤ s ≤ ∞ (see below for definitions), whose extrema may correspond to even distributions have been proposed. The starting point of this study is Problem 7 in [Smale 00] where the implications of the distribu...

The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc) on an ordinary set X, while for the second one the starting point are L-valued sets, that is a set equipped with some L-valued equality E : X × X → L (L being a lattice usuall...

In the final chain of the countable powerset functor, we show that the set at index ω1, regarded as a transition system, is not strongly extensional because it contains a “ghost” element that has no successor even though its component at index 1 is nonempty. For Jirka Adámek on his 70th birthday, with thanks for his many contributions and his inspiration.

Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner's construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as ...

By separating the principal acceptance mechanism from the concrete acceptance condition of a given Büchi automaton with n states, Schewe presented the construction of an equivalent deterministic Rabin transition automaton with o((1.65n)n) states via history trees, which can be simply translated to a standard Rabin automaton with o((2.26n)n) states. Apart from the inherent simplicity, Schewe’s c...