Günter Hotz

On the optimal layout of planar graphs with fixed boundary

The optimal planar layout of planar graphs with respect to the

On parsing coupled-context-free languages

L_1

Minimizing ROBDD sizes of incompletely specified Boolean functions by exploiting strong symmetries

- or

Eine Neue invariante für kontextfreie sprachen

L_2

Übertragung automatentheoretischer Sätze auf Chomsky-Sprachen

-metric leads to NP-hard problems, if one assumes the nodes of the graph to be fixed in the plane (see [FiPa], [Be]).In this paper we consider the (optimal) layout of graphs with fixed boundary (i.e., graphs, where only the nodes of a given cycle of the graph have fixed positions in the plane). The investigated layouts are straight line embeddings in a continuous part of the plane; the cost of a layout is calculated with help of very general cost functions including the pth power of the usual Euclidean distance metric for

Computability of Analytic Functions with Analytic Machines

p = 2,3, \cdots

SiLVIA-a simulation library for virtual reality applications

(for short,

Fast Uniform Analysis of Coupled-Context-Free Languages

l_p

A representation theorem of infinite dimensional algebras and applications to language theory

-metric).For a large class of graphs, which, for example, occur in chip layout problems as the abstract structure of switching circuits, we show the existence and uniqueness of the optimal layout.The main part of the paper is concerned with planar graphs. We get an interesting characterization of nonplanar layouts of planar graphs, which shows that the optimal layout of a ...

Representation Theorems for Analytic Machines and Computability of Analytic Functions

Abstract Coupled-Context-Free Grammars are a natural generalization of context-free grammars obtained by combining nonterminals to parentheses which can only be substituted simultaneously. Refering to the generative capacity of the grammars we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and all the languages generated by Tree Adjoining Grammars (TAGs) as the second element. The latter is important because today, TAGs are commonly used to model the syntax of natural languages. Here, we present an approach to analyse all language classes of the hierarchy uniformly. The distinct generative capacity of the subclasses is reflected in the time complexity of the algorithm which grows by the factor of the squared input length from one subclass to the next powerful one. For all our grammars, this complexity is only linear in its size which is dominating in case of the large grammars for natural languages, where the sentences are usually short. In addition, we show how to generate the normal form required by our algorithm and discuss subclasses which can be analysed faster than the general case.