Rewriting techniques are now recognized as a fundamental concept in many areas of computer science including mechanized theorem proving and operational semantics of programming languages. From a conceptual as well as operational point of view, the notion of rewrite rule application is crucial. It leads immediately to the concept of rewriting strategy which fully defines the way several rules ar...

Critical Pairs and Confluence of Arbitrary Binary Relations Rémy Haemmerlé and François Fages Projet Contraintes – INRIA Rocquencourt – France [email protected] Abstract. In a seminal paper, Huet introduced abstract properties of term rewriting systems, and the confluence analysis of terminating term rewriting systems by critical pairs computation. In this paper, we provide an abstrac...

In the standard theory of graph transformation, a rule modifies only subgraphs of constant size and fixed shape. The rules supported by the graph-rewriting tool GRGEN are far more expressive: they may modify subgraphs of unbounded size and variable shape. Therefore properties like termination and confluence cannot be analyzed as for the standard case. In order to lift such results, we formalize...

We address the issue of Ontology-Based Query Answering (OBQA), which seeks to exploit knowledge expressed in ontologies when querying data. Ontologies are represented in the framework of existential rules (aka Datalog±). A commonly used technique consists in rewriting queries into unions of conjunctive queries (UCQs). However, the obtained queries can be prohibitively large in practice. A well-...

Local confluence is an important property in many rewriting systems. The notion of critical pairs is central for being able to verify local confluence of rewriting systems in a static way. Critical pairs are defined already in the framework of graphs and adhesive rewriting systems. These systems may hold rules with or without negative application conditions. In this paper however, we consider r...

Chemical Genetic Programming (CGP) is a new method of genetic programming that introduced collision-based biochemical processes and realized dynamic mapping from genotypic strings to phenotypic trees. Chemical Genetic Programming (CGP) [1,2] proposes a new method of genetic programming that enables evolutionary optimization of the mapping from genotypic strings to phenotypic trees. The phenotyp...

The work reported here is part of the PROGRES (PROgrammed Graph Rewriting Systems) project. PROGRES is a very high level multi paradigm language for the specification of complex structured data types and their operations. The data structures are modelled as directed, attributed, node and edge labelled graphs (diane graphs). The basic programming constructs of PROGRES are graph rewriting rules (...

One of the most used algorithm in rewriting theory is the Knuth-Bendix completion procedure which starts from a terminating rewriting system and iteratively adds rules to it, trying to produce an equivalent convergent rewriting system. It is in particular used to study presentations of monoids, since normal forms of the rewriting system provide canonical representatives of words modulo the cong...

ROC! is a deterministic rewrite strategy language which includes the rewrite rulesas basic operators, and the deterministic choice and the repetition as high-level strategyoperators. In this paper we present a method which, for a given term rewriting system(TRS) R, constructs a new TRS R such that R-rewriting is equivalent (sound and com-plete) with R-rewriting constrained by RO...

We introduce a geometrical setting which seems promising for the study of computation in multiset rewriting systems, but could also be applied to register machines and other models of computation. This approach will be applied here to membrane systems (also known as P systems) without dynamical membrane creation. We discuss the rôle of maximum parallelism and further simplify our model by consi...