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.
7533318
Completeness of Context-Free Grammar Forms
The notions of a grammar form and g-interpretation were first introduced in [2]. However, it quickly became apparent, particularly for EOL forms [5], that (strict) interpretations had a wider interest as well as being better motivated mathematically. The study of parsing of grammar forms detailed in [4], the basic investigation in [8] on linear completeness amongst other results, the study of density in [9, lo] and the connections with graph theory shown in [ 1 l] have affirmed this position. The present paper continues the approach of [8] focussing on the characterization of complete grammar forms, that is grammar forms which generate all’ context-free languages. Some decidability problems will also be discussed. For further morivation and background material we refer the reader to [8, 141, while for all unexplained concepts in language theory, see [ 131. After giving the necessary definitions in the remainder of this section we characterize complete grammar forms in Section 2, 3 and 4. In Section 2 we introduce the central concept of expansion spectrum and in Section 3 the recently proved super normal form theorem [ 121, while in Section 4 the characterization is completed and generators and hierarchies are briefly mentioned. Consider context-free grammars G = (V, C, P, S), where Z is the alphabet of terminals, VZ the alphabet of nonterminals, P is the set of productions and
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.
21847551
Bounded Delay L Codes
Abstract Three natural notions of bounded delay for L codes are investigated. All interrelations, many of them rather surprising, between ordinary codes of bounded delay and L codes of bounded delay of various types are established.
12582971
Stabbing line segments
An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each ofn given line segments in the plane is presented. As a matter of fact, the algorithm computes a description of all stabbing lines. A purely geometric fact is proved which infers that this description requiresO(n) space to be specified. Our algorithm computes it inO(n logn) time which is optimal in the worst case.Using the description of the stabbing lines, we are able to decide inO(logn) time whether or not a specified line is a stabbing line. Finally, the problem of maintaining the description of all stabbing lines while inserting and deleting line segments is addressed.
33163861
Finitary and infinitary interpretations of languages
The main result of the paper can be viewed both as a generalization of a classical results concerning colorings of graphs, as well as a very useful over-all theorem from which various specific results concerning grammar and language families can be deduced. Essentially our main result says that, when considering infinitary families obtainable by inverse morphisms, it suffices to consider their finitary parts. Various applications are given, in particular, to grammar forms and context-free languages over infinite alphabets.
5762022
Orthogonal Drawings with Few Layers
In this paper, we study 3-dimensional orthogonal graph drawings. Motivated by the fact that only a limited number of layers is possible in VLSI technology, and also noting that a small number of layers is easier to parse for humans, we study drawings where one dimension is restricted to be very small. We give algorithms to obtain point-drawings with 3 layers and 4 bends per edge, and algorithms to obtain box-drawings with 2 layers and 2 bends per edge. Several other related results are included as well. Our constructions have optimal volume, which we prove by providing lower bounds.
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.
1804621
The Maximum Number of Edges in a Three-Dimensional Grid-Drawing
An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of threedimensional grid-drawings is obtained as a corollary. Our results generalise to the setting of multi-dimensional polyline grid-drawings.
206472202
Addressing Workload Variability in Architectural Simulations
The inherent variability of multithreaded commercial workloads can lead to incorrect results in architectural simulation studies. Although most architectural simulation studies ignore space variability's effects, our results demonstrate that space variability has serious implications for architectural simulation studies using multithreaded workloads. The standard solution - running long enough - does not easily apply to simulation because of its enormous slowdown. To address this problem, we propose a simulation methodology combining multiple simulations with standard statistical techniques, such as confidence intervals and hypothesis testing. This methodology greatly decreases the probability of drawing incorrect conclusions, and permits reasonable simulation times given sufficient simulation hosts.
341729
Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
In this paper we present the first non-trivial lower bounds for the total number of bends in 3-D orthogonal drawings of maximum degree six graphs. In particular, we prove lower bounds for the number of bends in 3-D orthogonal drawings of complete simple graphs and multigraphs, which are tight in most cases. These result are used as the basis for the construction of infinite classes of c-connected simple graphs and multigraphs (2 ≤ c ≤ 6) of maximum degree Δ (3 ≤ Δ ≤ 6) with lower bounds on the total number of bends for all members of the class. We also present lower bounds for the number of bends in general position 3-D orthogonal graph drawings. These results have significant ramifications for the '2-bends' problem, which is one of the most important open problems in the field.