40876494
Theory of 2-Structures
The process according to the present invention relates to the production of ferrovanadium alloys. The process comprises melting a charge containing iron and vanadium with a subsequent reduction of iron and vanadium to give a metal melt. In accordance with the present invention, iron and vanadium are reduced substantially completely. The resulting metal melt is poured into a converter and then purged, through the converter bottom, by means of oxygen blowing at a supply rate of oxygen and for a period of time sufficient to produce a slag containing at least 35% by weight of vanadium pentoxide. Thereafter, the metal melt is discharged from the converter, while vanadium and iron are reduced from the resulting slag by the metallothermal method.
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.
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.
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.
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).
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.
840154
Graph theoretic closure properties of the family of boundary NLC graph languages
SummaryNode 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). Boundary NLC (BNLC) grammars are NLC grammars with 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.
The present paper continues the investigations of basic properties of BNLC grammars and languages where the central question is the following: “If L is a BNLC language and P is a graph theoretic property, is the set of all graphs from L satisfying P again a BNLC language?” We demonstrate that the class of BNLC languages is very “stable” in the sense that for almost all properties we consider the resulting languages are BNLC. In particular, the above question gets an affirmative answer, if the property P is: being k-colorable, being connected, having a subgraph homeomorphic to a given graph, and being nonplanar.
206851807
Behaviour of Elementary Net Systems
38594002
Using String Languages to Describe Picture Languages
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.
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.