44960163
Restrictions on NLC Graph Grammars
Several models of ‘graph grammars’ have been studied with the objective of generating graphs from graphs using a finite set of derivation rules. In this way, possibly infinite sets of graphs (called graph languages) can be finitely defined. One aspect that must be addressed in any such model is the ‘embedding problem’, that is: When a production is applied, how does the new subgraph get reconnected to the original graph? Node-label controlled (NLC) grammars solve this problem in an elegant way that depends only on the labels of nodes in the new and original graphs. This paper examines certain restrictions on NLC grammars similar to the Chomsky or Greibach normal forms for context-free string grammars. For example, one restriction we consider requires each production to produce a terminal labeled node—similar to Greibach normal form. We also consider restrictions on the form which the embedding mechanism can take. Our result is that each of the restrictions we examine causes a reduction in generating power for the grammars. Finally, we discuss some directions for future research on NLC grammars.
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) .
43629107
On the Separating Power of Eol Systems
38741370
Repetitions in Homomorphisms and Languages
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
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.
34528489
Reductions for Primitive 2-Structures
A subset X of a 2-structure (a reversible edge-colored directed graph) g is a clan, if X cannot be distinguished by colors from outside of X. We show that if g is primitive, i.e. it has no nontrivial clans, then there exists an edge e or an end vertex x such that when e or x is removed from g, the resulting 2-structure g′ remains primitive. We also present a composition result for the unstable 2-structures, which are those primitive 2-structures where a removal of any edge results in a nonprimitive 2-structure.
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.
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.
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.