39074040
Pure Grammars
9628178
Uniform Interpretations of Grammar Forms
Encouraged by positive experiences with so-called uniform-interpretations of L-forms, we investigate in this paper a suitable analogous definition of uniform interpretations of grammar forms. Concerning CF grammar forms it is shown that a rich variety of language families can be obtained. CF grammar forms with a single variable are extensively examined both with regard to generative capacity (including a characterization of subregular, sublinear and subfinite index families) and with regard to the notion of goodness and badness. Concerning non-CF grammar forms it is shown that each of the families of EOL-, ETOL-, matrix-, scattered context-, context sensitive, type 0-languages (and many others) can be obtained by using interpretations of one form specific to this family.
39838781
Context-Free Grammar Forms with Strict Interpretations
This paper begins a systematic investigation of context-free grammar forms using the mechanism of “strict” interpretations: the interpretations of terminal letters are defined exactly as those of nonterminal letters. Thus, strict interpretations are more closely related to the master grammar than the g-interpretations investigated in the original grammar form paper [A. Cremers and S. Ginsburg, Context-free grammar forms, J. Comput. System Sci. 11 (1975), 86–116]. The main results of this paper concern reducibility, closure properties, generators and hierarchies of language families, as well as the characterization of grammar forms generating (under strict interpretation) the families of regular and linear languages.
1926264
L Codes and Number Systems
Abstract The notion of an L code is introduced as a generalization of the customary notion of a code. Attention is focused on unary L codes. where the target alphabet consists of one letter only. Unary L codes can be identified with such number systems where the representation is unique. Surprisingly many unary morphisms are L codes. Furthermore, even for non-L-codes there is only one ‘exceptional length’ We also give a complete classification for the binary case.
30874363
Synchronized EOL Forms Under Uniform Interpretation
— The aim ofthis paper is thejurther study oj EOLjorms under uniform interprétation. We are naturally led to the considération oj synchronized EOLjorms, which become the central thème of this paper. We prove: a ""strongest"" possible normaljorm resuit, the spanning normalJorm theorem; the non-existence oj uni-generatorsjor "reasonable" language amilies, which include thefinite, regular and context-jree j amilies; and a char act erization oj those ynchronized jorms which, under uniform interprétation, yield all regular languages. In closing we remark on three topics which are worthy oj separate investigation. Résumé. — Le but de cet article est de poursuivre l'étude des EOL-jormes sous des interprétations unijormes. Nous sommes conduits naturellement à considérer les EOL-jormes synchronisées qui deviennent le thème central de cet article. Nous établissons : un résultat sur la forme normale la plus « serrée » possible, le théorème sur la forme normale recouvrante, la non-existence d'uni-générateurs pour des jamilles « raisonnables » de langages qui comprennent les langages finis, rationnels et algébriques; et une caractérisation des formes synchronisées qui donnent, par interprétation unijorme, tous les langages rationnels. Pour terminer, nous effleurons trois domaines qui méritent une étude séparée.
5598249
MSW Spaces
52806192
Minimising the Number of Bends and Volume in 3-Dimensional
Orthogonal Graph Drawings with a Diagonal Vertex Layout
Abstract 
A 3-dimensional orthogonal drawing of a graph with maximum
degree at most 6, positions the vertices at grid-points in the 3-dimensional
orthogonal grid, and routes edges along grid-lines such that edge routes only
intersect at common end-vertices. Minimising the number of bends and the volume
of 3-dimensional orthogonal drawings are established criteria for measuring the
aesthetic quality of a given drawing. In this paper we present two algorithms
for producing 3-dimensional orthogonal graph drawings with the vertices
positioned along the main diagonal of a cube, so-called diagonal
drawings. This vertex-layout strategy was introduced in the 3-BENDS
algorithm of Eades et al. [Discrete Applied Math.
103:55–87, 2000]. We show that minimising the number of bends in a
diagonal drawing of a given graph is NP-hard. Our first algorithm minimises the
total number of bends for a fixed ordering of the vertices along the diagonal
in linear time. Using two heuristics for determining this vertex-ordering we
obtain upper bounds on the number of bends. Our second algorithm, which is a
variation of the above-mentioned 3-BENDS algorithm, produces 3-bend
drawings with n3+o(n3) volume, which is the best known upper bound for
the volume of 3-dimensional orthogonal graph drawings with at most three bends per
edge. 


14349700
Normal form algorithms for extended context-free grammars
We investigate the complexity of a variety of normal-form transformations for extended context-free grammars, where by extended we mean that the set of right-hand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of context-free objects just as Grail does for regular objects. Our results generalize known complexity bounds for context-free grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended context-free grammars (the symbol-threaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. Copyright 2001 Elsevier Science B.V.
44644050
Three-Dimensional Orthogonal Graph Drawing with Optimal Volume
In this paper, we study three-dimensional orthogonal box-drawings of graphs without loops. We provide lower bounds for three scenarios: (1) drawings where vertices have bounded aspect ratio, (2) drawings where the surface of vertices is proportional to their degree, and (3) drawings without any such restrictions. Then we give constructions that match the lower bounds in all scenarios within an order of magnitude.
122961893
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
13899040
The Regularity of Two-Way Nondeterministic Tree Automata Languages
We establish that regularly extended two-way nondeterministic tree automata with unranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets alphabets. We obtain this results by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is the Extensible Markup Language (XML), a metalanguage for defining document grammars. Such grammars have regular sets of right-hand sides for their productions and tree automata provide an alternative and useful modeling tool for them. In particular, we believe that they provide a useful computational model for what we call caterpillar expressions.