Basic Results for Two Types of High-Level Replacement Systems1 1Research partially supported by the European Community under TMR Network GETGRATS and the ESPRIT Working Group APPLIGRAPH.

AbstractThe general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M . Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M

Incremental update of constraint-compliant policy rules

Organizations typically define policies to describe (positive or negative) requirements about strategic objectives. Examples are policies relative to the security of information systems in general or to the control of access to an organization’s resources. Often, the form used to specify policies is in terms of general constraints (what and why) to be enforced via the use of rules (how and when). The consistency of the rule system (transforming valid states into valid states) can be compromised and rules can violate some constraints when constraints are updated due to changing requirements. Here, we explore a number of issues related to constraint update, in particular proposing a systematic way to update rules as a consequence of modifications of constraints, by identifying which components of the rule have to be updated. Moreover, we show the construction of sets of rules, directly derived from a positive constraint, to guarantee constraint preservation and constraint enforcement

Incremental update of constraint-compliant policy rules

Organizations typically define policies to describe (positive or negative) requirements about strategic objectives. Examples are policies relative to the security of information systems in general or to the control of access to an organization’s resources. Often, the form used to specify policies is in terms of general constraints (what and why) to be enforced via the use of rules (how and when). The consistency of the rule system (transforming valid states into valid states) can be compromised and rules can violate some constraints when constraints are updated due to changing requirements. Here, we explore a number of issues related to constraint update, in particular proposing a systematic way to update rules as a consequence of modifications of constraints, by identifying which components of the rule have to be updated. Moreover, we show the construction of sets of rules, directly derived from a positive constraint, to guarantee constraint preservation and constraint enforcement

Hierarchical Graph Transformation

If systems are specified by graph transformation, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from at to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow to copy and to remove hierarchical subgraphs in a single rule application

Logic Programming as Hypergraph Rewriting

Logic Programming and (Hyper-)Graph Rewriting are two well known fields of Computer Science. In this paper we show how to model logic program computations through algebraic techniques familiar to the graph rewriting community. Clauses of a logic program are represented by graph productions, goals by suitable hypergraphs (called jungles), and resolution steps by an algebraic construction involving three pushouts. The correspondence between the two formalisms is further analyzed by providing a precise algebraic characterization of specialization and unfolding of clauses

High Level Replacement Systems applied to algebraic specifications and petri nets

World Scientifi

On a Uniform Representation of Transformation Systems

We discuss an intermediate language to represent transitions defining behaviours of autonomous agents. The language allows a uniform representation of several diagrammatic languages for specification of reactive systems, based on an underlying notion of transition. The translation of graph transformations to this language opens an opportunity for a notion of communication between agents represented by graphs