34951842
Primitivity is Hereditary for 2-Structures
Abstract It is proved that each primitive 2-structure on n elements ( n ⩾3) contains a primitive substructure on either ( n −1) or ( n −2) elements.
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).
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.
39431424
Incremental construction of 2-structures
Abstract A labeled 2-structure g is an edge-labeled directed graph with a reversibility condition on the labels. Each labeled 2-structure g can be represented as a tree, the prime tree of g. We characterize a labeled 2-structure h in terms of the prime tree of a labeled 2-structure g which results from h by removing one element from h. This leads to an O(n3) algorithm for the construction of the prime tree.
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.
13303483
Theory of Traces
Abstract The theory of traces , originated by A. Mazurkiewicz in 1977, is an attempt to provide a mathematical description of the behavior of concurrent systems. Its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand. One can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role. Alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs (or even in the theory of labeled partial orders). This paper attempts to present a major portion of the theory of traces in a unified way. However, it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved. Although traditionally most of the development in the theory of traces follows the string-language-theoretic line, we try to demonstrate to the reader that the graph-theoretic point of view may be more appropriate. The paper essentially consists of two parts. The first one (Sections 1 through 4) is concerned with the basic theory of traces. The second one (Section 5) presents applications of the theory of traces to the theory of the behavior of concurrent systems, where the basic system model we have chosen is the condition/event system introduced by C.A. Petri.
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.
37152120
Transition Systems, Event Structures and Unfoldings
A subclass of transition systems called elementary transition systems can be identified with the help of axioms based on a structural notion called regions. Elementary transition systems have been shown to be the transition system model of a basic system model of net theory called elementary net systems. Here we show that by smoothly strengthening the regional axioms for elementary transition systems, one obtains a subclass called occurrence transition system. We then prove that occurrence transition systems are the transition system model of yet another basic model of concurrency, namely, prime event structures. We then propose an operation of unfolding elementary transition systems into occurrence transition systems, We prove that it is "correct" in a strong categorical sense.
36510403
On Coordinated Selective Substitutions: Towards a Unified Theory of Grammars and Machines
Abstract The notion of a coordinated table selective substitution system (a cts system ) is introduced. It provides a unifying framework for both grammars and machines (automata) and hence a really broad framework for formal language theory. An extensive number of examples is given which illustrate how a quite considerable number of grammars and automata considered in the literature may be ‘naturally’ interpreted as special instances (subclasses of the class) of cts systems.
43370814
Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity
Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs) which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Here we consider a restriction of NLC grammars, so-called boundary NLC (BNLC) grammars , distinguished by the property that whenever in a graph already generated two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages . Although we show that this restriction leads to a smaller class of languages, still enough generative power remains to define interesting graph languages. For example, trees, complete bipartite graphs, maximal outerplanar graphs, k -trees, graphs of bandwidth ⩽ k , graphs of cyclic bandwidth ⩽ k , graphs of binary tree bandwidth ⩽ k , graphs of cutwidth ⩽ k (always for a fixed positive integer k ) turn out all to be BNLC languages. We prove a number of normal forms for BNLC grammars and then we indicate their usefulness by various applications. In particular, we show that for connected graphs of bounded degree the membership problem for BNLC languages is solvable in deterministic polynomial time.
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) .