1753130
Conditions Enforcing Regularity of Context-Free Languages
2026601
Elementary Net Systems
9307461
Context Free Normal Systems and ETOL Systems
Abstract The relationship between extended context free normal systems (a nondeterministic version of Tag systems of Post with deletion number equal to 1 and using nonterminals) and ETOL systems is considered. It is demonstrated that the class of languages generated by context free normal systems (denoted L (ECFN)) lies strictly between the clas of EOL languages (denoted L (EOL)) and the class of ETOL languages. Several characterizations of L (ECFN)) in terms of L (EOL)) are provided and a number of closure properties of L '(ECFN) are established.
27704198
Nonterminals versus homomorphisms in defining languages for some classes of rewriting systems
AbstractGiven a rewriting system G (its alphabet, the set of productions and the axiom) one can define the language of G by(i)taking out of all strings generated by G only those which are over a distinguished subalphabet of G, or(ii)translating the set of all strings generated by G by a fixed homomorphism.
The “trade-offs” between these two mechanisms for defining languages are discussed for both “parallel” rewriting systems from the developmental systems hierarchy and “sequential” rewriting systems from the Chomsky hierarchy.
206851807
Behaviour of Elementary Net Systems
8298605
Partial (set) 2-structures
SummaryWe continue the investigation of labeled partial (set) 2-structures initiated in [5] and in particular we explore applications to the theory of net-based concurrent systems. The problem of characterizing state spaces of basic classes of Petri nets, and the problem of synthesizing state spaces of basic classes of Petri nets from their “abstract” descriptions in the form of directed edge-labeled graphs are investigated.
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.
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.
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.
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).