Kruskal's Tree Theorem for Acyclic Term Graphs

In this paper we study termination of term graph rewriting, where we restrict our attention to acyclic term graphs. Motivated by earlier work by Plump we aim at a definition of the notion of simplification order for acyclic term graphs. For this we adapt the homeomorphic embedding relation to term graphs. In contrast to earlier extensions, our notion is inspired by morphisms. Based on this, we establish a variant of Kruskal's Tree Theorem formulated for acyclic term graphs. In proof, we rely on the new notion of embedding and follow Nash-Williams' minimal bad sequence argument. Finally, we propose a variant of the lexicographic path order for acyclic term graphs.Comment: In Proceedings TERMGRAPH 2016, arXiv:1609.0301

Well-founded Path Orderings for Drags

International audienceThe definition herein of the Graph Path Ordering (GPO) on certain graph expressions is inspired by that of the Recursive Path Ordering (RPO), and enjoys all those properties that have made RPO popular, in particular, well-foundedness and monotonicity on variable-free terms.We are indeed interested in a generalization of algebraic expressions called operadic expressions, which are finite graphs each vertex of which is labelled by a function symbol, the arity of which governs the number of vertices it relates to in the graph. These graphs are seen here as terms with sharing and back-arrows. Operadic expressions arethemselves multiplied (an associative operation) to form monomials, which are in turn summed up (an associative commutative operation) to form polynomials. Operadic expressions and their polynomials occur in algebraic topology, and in various areas of computer science, notably concurrency and type theory. Rewriting basic operadic expressions isvery much like rewriting algebraic expressions, while rewriting their monomials and polynomials is very much like the Groebner basis theory. GPO provides an initial building block for computing with operadic expressions and their polynomials

Complexity of Acyclic Term Graph Rewriting

Term rewriting has been used as a formal model to reason about the complexity of logic, functional, and imperative programs. In contrast to term rewriting, term graph rewriting permits sharing of common sub-expressions, and consequently is able to capture more closely reasonable implementations of rule based languages. However, the automated complexity analysis of term graph rewriting has received little to no attention. With this work, we provide first steps towards overcoming this situation. We present adaptions of two prominent complexity techniques from term rewriting, viz, the interpretation method and dependency tuples. Our adaptions are non-trivial, in the sense that they can observe not only term but also graph structures, i.e. take sharing into account. In turn, the developed methods allow us to more precisely estimate the runtime complexity of programs where sharing of sub-expressions is essential

Termination of Graph Transformation Systems Using Weighted Subgraph Counting

We introduce a termination method for the algebraic graph transformation framework PBPO+, in which we weigh objects by summing a class of weighted morphisms targeting them. The method is well-defined in rm-adhesive quasitoposes (which include toposes and therefore many graph categories of interest), and is applicable to non-linear rules. The method is also defined for other frameworks, including SqPO and left-linear DPO, because we have previously shown that they are naturally encodable into PBPO+ in the quasitopos setting. We have implemented our method, and the implementation includes a REPL that can be used for guiding relative termination proofs.Comment: 36 pages. Preprint submitted to LMCS. Extends the conference version published at the 16th International Conference on Graph Transformation (ICGT 2023

On termination of Graph Rewriting Systems through language theory

The termination issue we tackle is rooted in natural language processing where graph rewriting systems (GRS) may contain a large number of rules, often in the order of thousands. Decidable concepts thus become mandatory to verify the termination of such systems. The notion of graph rewriting consider does not make any assumption on the structure of graphs (they are not “term graphs”, “port graphs” nor drags). The lack of algebraic structure in our setting led us to proposing two orders on graphs inspired from language theory: the matrix multiset-path order and the rational embedding order. We show that both are stable by context, which we then use to obtain the main contribution of the paper: under a suitable notion of “interpretation”, a GRS is terminating if and only if it is compatible with an interpretation

Termination of graph rewriting systems through language theory

International audienceThe termination issue that we tackle is rooted in Natural Language Processing where computations are performed by graph rewriting systems (GRS) that may contain a large number of rules, often in the order of thousands. This asks for algorithmic procedures to verify the termination of such systems. The notion of graph rewriting that we consider does not make any assumption on the structure of graphs (they are not "term graphs", "port graphs" nor "drags"). This lack of algebraic structure led us to proposing two orders on graphs inspired from language theory: the matrix multiset-path order and the rational embedding order. We show that both are stable by context, which we then use to obtain the main contribution of the paper: under a suitable notion of "interpretation", a GRS is terminating if and only if it is compatible with an interpretation

Gobierno electrónico y simplificación administrativa de la Gerencia de Desarrollo Urbano de la Municipalidad Distrital de Nuevo Chimbote, 2022

El estudio tuvo como objetivo, determinar la relación entre el gobierno electrónico y la simplificación administrativa en la Gerencia de Desarrollo Urbano de la Municipalidad Distrital de Nuevo Chimbote, 2022. El tipo de estudio, según su nivel de alcance es correlacional, cuyo diseño de estudio es no experimental, transversal, descriptivo correlacional. Se trabajó con una muestra probabilística y técnica de muestreo aleatorio simple, constituida por 115 usuarios. Para la recolección de datos se utilizó la técnica de la encuesta y mediante la aplicación de los instrumentos: cuestionario “Gobierno electrónico” y el cuestionario “Simplificación administrativa”, se recolectaron datos, que fueron analizados mediante tablas de frecuencias, diagrama de barras, tablas de contingencia y la prueba paramétrica R de Pearson. Entre sus resultados, se determinó que, el control interno es percibido como regular por el 53.9 % de usuarios y a la vez la simplificación administrativa como medianamente eficiente por el 50.4 % de usuarios. Concluyendo, que existe una relación directa de nivel alta (Rho=0,777) y significativa (P-valor 0,000 < 0,05) entre el gobierno electrónico y la simplificación administrativa