Showing papers by "Grzegorz Rozenberg published in 1982"
TL;DR: This paper investigates the basic properties of pictures and picture description languages from the formal language theory point of view.
Abstract: A picture is a set of unit lines from the Cartesian plane considered as a square grid. A word over the alphabet l, r, u, d is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l, r, u, d, is: l go one unit line to the left of the current point r go one unit line to the right of the current point u go one unit line up from the current point, and d go one unit line down from the current point. A set of picture descriptions forms a picture description language. This paper investigates the basic properties of pictures and picture description languages from the formal language theory point of view.
103 citations
TL;DR: This paper considers a possible classification of embedding mechanisms for (node-rewriting) graph grammars, which allows one to fit a number of existing notions of a graph grammar into a common framework and points out new “natural” possibilities for defining the embedding mechanism in a graph Grammar.
89 citations
84 citations
04 Oct 1982
TL;DR: This work presents a tutorial introduction to the algebraic approach of graph grammars based on double and single pushouts, and describes Gottler's operational graph Grammars with pushouts.
46 citations
TL;DR: Two embedding mechanisms used in graph grammars are discussed and compared: a connection relation mechanism ( introduced in Janssens and Rozenberg) and a stencil mechanism (introduced in Culik and Lindenmayer).
45 citations
27 Sep 1982
TL;DR: Formal language theory is used to some extent in the investigation of properties of Petri nets and the language of a Petri net consists of the set of all firing sequences (or only of those firing sequences that lead to one of the finite number of final markings).
Abstract: Formal language theory is used to some extent in the investigation of properties of Petri nets (see, e.g. [H], [JV] and [P]). In most applications of language theory for Petri nets one considers completely sequentialized versions of Petri nets only. That is one assumes that a Petri net has one central run place which allows only a single transition to fire at a time; any sequence of such firings is called a firing sequence and the language of a Petri net consists of the set of all firing sequences (or only of those firing sequences that lead to one of the finite number of final markings).
38 citations
04 Oct 1982
36 citations
TL;DR: This study investigates the relationship between nk(K) and nK where Kis a language and h is a homorphism, and investigates the relations existant entre KH(K), nKi où K est un langage and h est un homomorphisme.
Abstract: — The subword complexity of a language K is the function nK on positive integer s such that nK (n) equals the number of different subwords of length n appearing in words of X. We investigate the relationship between nk(K) and nK where Kis a language and h is a homorphism. This study is aiso carried out for the special case when Kis a DOL language. Resumé. — La complexité des facteurs d'un langage K est la fonction nK définie sur les entiers positifs telle que nK (n) est le nombre de facteurs distincts de longueur n apparaissant dans les mots de K. Nous étudions les relations existant entre KH(K) et nKi où K est un langage et h est un homomorphisme. Cette étude est menée également dans le cas particulier où Kest un DOL langage.
23 citations
04 Oct 1982
TL;DR: A word over the alphabet {l,r,u,d} is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l, r, u,d is: l — go (and draw) one unit line to the left of the current point.
Abstract: A picture is a connected set of axis parallel unit lines from the Cartesian plane considered as a square grid. A word over the alphabet {l,r,u,d} is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l,r,u,d is: l — go (and draw) one unit line to the left of the current point; r,u, and d are interpreted analogously with “left” replaced by “right”, “up”, and “down”, respectively. This is one of the chain codemodels.
22 citations
TL;DR: This paper provides a motivation for considering this particular model for the generation of division patterns in cell layers, formal aspects of this model are discussed, and its implementation is presented.
20 citations
04 Oct 1982
TL;DR: This paper aims to provide a solid formal foundation to the study of concurrency problems that arise within the area of graph grammars and think it is possible and fruitful to apply the concepts and techniques of net theory to these problems.
Abstract: Firstly, net theory, which is a well established theory of distributed systems and processes [I] relies heavily on a graphical notation. One of the strengths of this theory is that many of the fundamental notions concerning concurrent systems and in particular, the dynamics of a concurrent systemcan be made transparent with the help of simple net diagrams and transformations of such diagrams. It is important to provide a solid formal foundation to this aspect of net theory and graph grammars appear to be the obvious tool for doing so. The second motivation is that in the study of concurrency problems that arise within the area of graph grammars [2] we think it is possible and fruitful to apply the concepts and techniques of net theory.
12 Jul 1982
12 Jul 1982
TL;DR: It is proved that given an E0L form F it is decidable whether or not F is vomplete and the concept of n-completeness, n a positive integer, is introduced and it is shown that it is equivalent with n- completeness.
Abstract: It is proved that given an E0L form F it is decidable whether or not F is vomplete. The concept of n-completeness, n a positive integer, is introduced and it is shown that for an E0L form F and an integer n?2 vompleteness is equivalent with n-completeness.
TL;DR: In this paper, the decidability status of several properties of derivations in E0L systems (forms) has been investigated and it has been shown that the so-called one-to-many simulation is decidable.
04 Oct 1982
TL;DR: This paper presents an attempt to develop the same type of methodology for defining graph languages as previous work on hypergraphs, and discusses the use of one hypergraph to define a (possibly infinite) set of graphs.
Abstract: The notion of a finite automaton is perhaps the most basic notion of formal language theory. Each finite automaton is (can be represented by) a graph and it defines the set of strings referred to as the languageof the automaton. Thus we have here the situation where one graph is used to define a (possibly infinite) set of strings. In other words, one 'higher type" object is used to define a set of "lower type" objects certainly in general graphs have a more involved structure than strings. In this paper we present an attempt to develop the same type of methodology for defining graph languages. A hypergraph (see, e.g. [B] ), is a structure generalizing the notion of a graph. We will discuss the use of one hypergraph to define a (possibly infinite) set of graphs. (Actually the structure we use is more general than a hypergraph it is a hypergraph equipped with an extra graph structure.) Various grain-generating systems based on the use of hypergraphs are introduced and their properties (included the properties of classes of languages they define) are discussed. We point out also the relationship of these systems to the theory of Petri nets. The paper presents only part of the results concerning the theory of hypergraph-based systems.
TL;DR: It is demonstrated that every context-free language is a homomorphic image of the intersection of two DOS languages and that every recursively enumerable language is the homomorphic images of the intersections of three DOS languages.
Journal Article•
01 Jan 1982
01 Jan 1982
TL;DR: This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.
Abstract: Abstract Let Σ be an arbitrary fixed alphabet. The direct copying relation (over Σ+) is a binary relation defined by: x copy y if and only if x = x1ux2 and y = x1uux2 for some words x1,x2,u where u is nonempty. The copying relation copy∗ is defined as the reflexive and transitive closure of copy. A copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵΣ + : w copy ∗ z} , it is referred to as a copy language. This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.
Proceedings Article•
27 Sep 1982
TL;DR: This note demonstrates the existence of E0L forms F and G which are n -similar, i.e. L n = L n ( F) but L n +1 ( F )≠ L n -1 ( G) for n ∈ {2, 3}.
TL;DR: The generative capacity of the different mechanisms of EOL form interpretations is considered and new mechanisms which deal with uniformity are introduced and investigated.