205092173
CTS Systems and Petri Nets
The general theory of coordinated table selective substitution systems (cts systems for short) (see Rozenberg (1985)), provides a unifying framework for a considerable number of grammar and automaton models considered in the literature. This paper is mainly devoted to the investigation of a- natural subclass of cts systems (which uses the 'context-free grammar selector' for its memory access) and it turns out that this subclass closely corresponds to the Petri net model of concurrent processes.
43629107
On the Separating Power of Eol Systems
39400225
On Subword Complexities of Homomorphic Images of Languages
— 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.
38741370
Repetitions in Homomorphisms and Languages
17444444
The Bounded Degree Problem for NLC Grammars is Decidable
Abstract The degree of a graph H is the maximum among the degrees of its nodes. A set of graphs L is of bounded degree if there exists a positive integer n such that the degree of each graph in L does not exceed n . We demonstrate that it is decidable whether or not the (graph) language of an arbitrary node label controlled (NLC) grammar is of bounded degree. Moreover, it is shown that, given an arbitrary NLC grammar G generating the language L(G) of bounded degree, one can effectively compute the maximum integer which appears as the degree of a graph in L(G) .
21626854
An Observation on Scattered Grammars
Scattered context-grammars were introduced in [ 1 j. They constitute one of the most interesting examples of string rewriting systems that are ‘context-dependent’. However they form one of the least understood types of grammars. Although the relationship of (some of the varier.-.._ _ -+i-~ of! the class of scattered context grammars to some classes of languages was studied (see e.g. [2,31) the main question remains open: Do scattered context grammars generate all context sensitive languages’! Clearly an answer to this question would shed light on the role that context plays in grammars. In this work we show that recursively enumerable languages possess a very strong representation in the class of scattered context languages. As a matter of fact it is well known th!at they possess the same representation in the class of context sensitive languages! Thus a result of this form supports in some sense the conjecture that the class of scattered context languages equals the class of context sensitive languages. In any case it says that the class of scattered context languages is ‘close to’ the class of context sensitive languages. Since we provide a direct proof of !2!r reslult (an explicit construction is given) it gives some insight iI& how scattered grammars work. We assume the reader to be familiar with Post Ilormal systems (e.g. in the scope of [4j). If H is a Post normal system, c4 is its axiom and al$ --) S&, ar*S --, S& are productions of l-l, then wr zlrssume that loill = ia21 SK Iwl and Ipli, l&l >O. The language of H consists of al! the words over its alphabet for which
37770747
Transitivity of local complementation and switching on graphs
Abstract The operations complementation C , local complementation λ x , and switching σ x for the vertices x of a finite undirected graph are considered. The operation λ x complements the subgraph induced by the neighbourhood of x in the given graph, and the switching σ x changes the neighbourhood of x to its complement vertex set. It is proved that the compositions δ x = λ x C (for vertices x ∈ D ) generate a transitive group on the graphs with vertex set D , that is, for any two graphs g and h on D , there exists a composition α of operations δ x such that h = α ( g ). It is also shown that the compositions τ x = λ x σ x (for x ∈ D ) generate a transitive group on the graphs.
6414809
Developmental systems and languages
Developmental systems were introduced (Lindenmayer, 1968, 1971) in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms. These systems were originally conceived as linear arrays of interconnected finite automata, each automaton corresponding to a living cell, with the possibility that new automata can be added to the array (cells divide) or be deleted from the array (cells die).
 Each cell in the array is supposed to have the same state-transition and output functions. As required by biological considerations these functions must be applied to all cells in the array simultaneously at each time step. Thus one obtains infinite sequences of arrays once the functions and the initial arrays are specified. Simplified constructs are defined (and used in this paper) by considering the states and outputs to be identical and thus omitting the output functions. Such filamentous developmental systems have been called “Lindenmayer models” Herman, 1969, 1970) or “L-systems” (Van Dalen, 1971).
9443958
Dynamic change within workflow systems
Dynamic change is a large and pervasive unsolved problem which surfaces within office systems as well as within software engineering, manufacturing, and numerous other domains. Procedural changes, performed in an ad hoc manner, can cause inefficiencies, inconsistencies, and catastrophic breakdowns within offices. This paper is concerned with dynamic change to procedures in the context of workflow systems. How can we make workflow systems more flexible and open? We believe that part of the answer lies in the study and solution of the dynamic change problem. In this paper, we use a Petri net formalism to analyze structural change within office procedures. As an example, we define a class of change called “synthetic cut-over change”, and apply our formalism to prove that this class maintains correctness when downsizing occurs.
12269815
Angular 2-Structures
The theory of 2-structures forms a convenient framework for investigating graphs. In this paper we investigate the class of angular 2-structures which results by requiring that the primitivity is forbidden on the lowest possible level, i.e. it is required that no substructure on three elements is primitive. The paper presents the basic theory of angular 2-structures and, in particular, the theory of primitive angular 2-structures. We demonstrate that the notion of an angular 2-structure is a well-chosen generalization of the notions of a symmetric graph and a partial order.
33004065
Pancyclicity in switching classes
Abstract Switching classes of graphs were introduced by van Lint and Seidel in the context of equiangular lines in elliptic geometry. We show that every switching class, except the class of all complete bipartite graphs, contains a pancyclic graph. This implies that deciding whether a switching class contains a hamiltonian graph can be done in polynomial time (as was noted by Kratochvil et al. (1992)) although this problem is NP-complete for graphs.