9788732
On generators and generative capacity of EOL forms
SummaryIn this paper we study the generative capacity of EOL forms from two different points of view. On the one hand, we consider the generative capacity of special EOL forms which one could call ‘linear like’ and ‘context free like’, establishing the existence of a rich variety of non-regular sub-EOL language families. On the other hand, we propose the notion of a ‘generator’ L of a language family ℒ We mean by this that any synchronized EOL system generating L generates — if understood as an EOL form — all languages of ℒ. We characterize the generators of the family of regular languages, and prove that other well known language families do not have generators.
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.
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
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.
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.
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.
8790131
Three-Dimensional 1-Bend Graph Drawings
We consider three-dimensional grid-drawings of graphs with at most one bend per edge. Under the additional requirement that the vertices be collinear, we prove that the minimum volume of such a drawing is ( cn), where n is the number of vertices and c is the cutwidth of the graph. We then prove that every graph has a three-dimensional grid-drawing with O(n 3 = log 2 n) volume and one bend per edge. The best previous bound was O(n 3 ).
12937575
Application-specific protocols for user-level shared memory
Recent distributed shared memory (DSM) systems and proposed shared-memory machines have implemented some or all of their cache coherence protocols in software. One way to exploit the flexibility of this software is to tailor a coherence protocol to match an application's communication patterns and memory semantics. This paper presents evidence that this approach can lead to large performance improvements. It shows that application-specific protocols substantially improved the performance of three application programs-appbt, em3d, and barnes-over carefully tuned transparent shared memory implementations. The speed-ups were obtained on Blizzard, a fine-grained DSM system running on a 32-node Thinking Machines CM-5.<<ETX>>
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.
12379809
Degree constrained book embeddings
A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G = (V, E), let f : V → N be a function such that 1 ≤ f(v) ≤ deg(v). We present a Las Vegas algorithm which produces a book embedding of G with O(√|E|.maxv ⌈deg(v)/f(v)⌉) pages, such that at most f(v) edges incident to a vertex v are on a single page. This result generalises that of Malitz [J. Algorithms 17 (1) (1994) 71-84].
1943361
Modeling cost/performance of a parallel computer simulator
This article examines the cost/performance of simulating a hypothetical target parallel computer using a commercial host parallel computer. We address the question of whether parallel simulation is simply faster than sequential simulation, or if it is also more cost-effective. To answer this, we develop a performance model of the Wisconsin Wind Tunnel (WWT), a system that simulates cache-coherent shared-memory machines on a message-passing Thinking Machines CM-5. The performance model uses Kruskal and Weiss's fork-join model to account for the effect of event processing time variability on WWT's conservative fixed-window simulation algorithm. A generalization of Thiebaut and Stone's footprint model accurately predicts the effect of cache interference on the CM-5. The model is calibrated using parameters extracted from a fully parallel simulation (p = N), and validated by measuring the speedup as the number of processors (p) ranges from 1 to the number of target nodes (N). Together with simple cost models, the performance model indicates that for target system sizes of 32 nodes and larger, parallel simulation is more cost-effective than sequential simulation. The key intuition behind this result is that large simulations require large memories, which dominate the cost of a uniprocessor; parallel computers allow multiple processors to simultaneously access this large memory.