Experimenting with Reaction Systems using Graph Transformation and GROOVE

Graph transformation systems have been studied extensively and applied to several areas of computer science like formal language theory, the modeling of databases, concurrent or distributed systems, and visual, logical, and functional programming. In most kinds of applications it is necessary to have the possibility of restricting the applicability of rules. This is usually done by means of application conditions. In this paper, we continue the work of extending the fundamental theory of graph transformation to the case where rules may use arbitrary (nested) application conditions. More precisely, we generalize the Embedding theorem, and we study how local confluence can be checked in this context. In particular, we define a new notion of critical pair which allows us to formulate and prove a Local Confluence Theorem for the general case of rules with nested application conditions. All our results are presented, not for a specific class of graphs, but for any arbitrary M-adhesive category, which means that our results apply to most kinds of graphical structures. We demonstrate our theory on the modeling of an elevator control by a typed graph transformation system with positive and negative application conditions.

With rising complexity of today's software and hardware systems and the hypothesized increase in autonomous, intelligent, and self-* systems, developing correct systems remains an important challenge. Testing, although an important part of the development and maintainance process, cannot usually establish the definite correctness of a software or hardware system - especially when systems have arbitrarily large or infinite state spaces or an infinite number of initial states. This is where formal verification comes in: given a representation of the system in question in a formal framework, verification approaches and tools can be used to establish the system's adherence to its similarly formalized specification, and to complement testing. One such formal framework is the field of graphs and graph transformation systems. Both are powerful formalisms with well-established foundations and ongoing research that can be used to describe complex hardware or software systems with varying degrees of abstraction. Since their inception in the 1970s, graph transformation systems have continuously evolved; related research spans extensions of expressive power, graph algorithms, and their implementation, application scenarios, or verification approaches, to name just a few topics. This thesis focuses on a verification approach for graph transformation systems called k-inductive invariant checking, which is an extension of previous work on 1-inductive invariant checking. Instead of exhaustively computing a system's state space, which is a common approach in model checking, 1-inductive invariant checking symbolically analyzes graph transformation rules - i.e. system behavior - in order to draw conclusions with respect to the validity of graph constraints in the system's state space. The approach is based on an inductive argument: if a system's initial state satisfies a graph constraint and if all rules preserve that constraint's validity, we can conclude the constraint's validity in the system's entire state space - without having to compute it. However, inductive invariant checking also comes with a specific drawback: the locality of graph transformation rules leads to a lack of context information during the symbolic analysis of potential rule applications. This thesis argues that this lack of context can be partly addressed by using k-induction instead of 1-induction. A k-inductive invariant is a graph constraint whose validity in a path of k-1 rule applications implies its validity after any subsequent rule application - as opposed to a 1-inductive invariant where only one rule application is taken into account. Considering a path of transformations then accumulates more context of the graph rules' applications. As such, this thesis extends existing research and implementation on 1-inductive invariant checking for graph transformation systems to k-induction. In addition, it proposes a technique to perform the base case of the inductive argument in a symbolic fashion, which allows verification of systems with an infinite set of initial states. Both k-inductive invariant checking and its base case are described in formal terms. Based on that, this thesis formulates theorems and constructions to apply this general verification approach for typed graph transformation systems and nested graph constraints - and to formally prove the approach's correctness. Since unrestricted graph constraints may lead to non-termination or impracticably high execution times given a hypothetical implementation, this thesis also presents a restricted verification approach, which limits the form of graph transformation systems and graph constraints. It is formalized, proven correct, and its procedures terminate by construction. This restricted approach has been implemented in an automated tool and has been evaluated with respect to its applicability to test cases, its performance, and its degree of completeness.

In this paper we present several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. In our approach a computational mesh is represented by a composite graph and mesh operations are expressed by the graph transformation rules. Each graph transformation system is responsible for different kind of operations. In particular, there is a graph transformation system expressing generation of an initial mesh, generating element matrices and elimination trees for interfacing with direct solver algorithm, a graph transformation system deciding which elements have to be further refined, as well as a graph transformation system responsible for execution of mesh refinements. These graph transformation systems are tested using a graph transformation tool (called GRAGRA), which provides a graphical environment for defining graphs, graph transformation rules and graph transformation systems. In this paper we illustrate the concepts by using an exemplary derivation for a three dimensional projection problem, based on a set of graph transformation rules.

The integrated development environment AGG supports the specification of algebraic graph transformation systems based on attributed, typed graphs with node type inheritance, graph rules with application conditions, and graph constraints. It offers several analysis techniques for graph transformation systems including graph parsing, consistency checking of graphs as well as conflict and dependency detection in transformations by critical pair analysis of graph rules, an important instrument to support the confluence check of graph transformation systems. AGG 2.0 includes various new features added over the past two years. It supports the specification of complex control structures for rule application comprising the definition of control and object flow for rule sequences and nested application conditions. Furthermore, new possibilities for constructing rules from existing ones (e.g., inverse, minimal, amalgamated, and concurrent rules) and for more flexible usability of critical pair analyses have been realized.Keywordsgraph transformation toolAGG 2.0

Joint Optimization and Reachability Analysis in Graph Transformation Systems with Time

Preface: UNIGRA'03 - Uniform Approaches to Graphical Process Specification Techniques

The “classical” approach to represent Petri nets by graph transformation systems is to translate each transition of a specific Petri net to a graph rule (behavior rule). This translation depends on a concrete model and may yield large graph transformation systems as the number of rules depends directly on the number of transitions in the net. Hence, the aim of this paper is to define the behavior of Algebraic High-Level nets, a high-level Petri net variant, by a parallel, typed, attributed graph transformation system. Such a general parallel transformation system for AHL nets replaces the translation of transitions of specific AHL nets. After reviewing the formal definitions of AHL nets and parallel attributed graph transformation, we formalize the classical translation from AHL nets to graph transformation systems and prove the correctness of the translation. The translation approach then is contrasted to a definition for AHL net behavior based on parallel graph transformation. We show that the resulting amalgamated rules correspond to the behavior rules from the classical translation approach.KeywordsGraph TransformationPartial CoveringInteraction SchemeGraph GrammarRule SchemeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Graph Transformation Systems (GTSs) provide visual and explicit semantics for dynamically evolving multi-process systems such as network programs and communication protocols. Existing symmetry reduction techniques that generate a reduced, bisimilar model for alleviating state explosion in model checking are not applicable to dynamic models such as those given by GTSs. We develop symmetry reduction techniques applicable to evolving GTS models and the programs that generate them. We also provide an on-the-fly algorithm for generating a symmetry-reduced quotient model directly from a set of graph transformation rules. The generated quotient model is GTS-bisimilar to the model under verification and may be exponentially smaller than that model. Thus, analysis of the system model can be performed by checking the smaller GTS-bisimilar model.

The main idea of graph grammars and graph transformation is the rule-based graph rewriting, where the application of every rule graph rule leads to a graph transformation step. Graph grammars can be used to generate graph languages which is similar to Chomsky grammars in formal language theory. Moreover, graphs can be used to model the states of all kinds of systems, which allows one to use graph transformation to model state changes in these systems. A rule-based transformation system may show two kinds of nondeterminism: (1) for each rule can exist several matches, and (2) several rules can be applicable. This paper concentrates on the second non-determinism, studying a method to detect the rules which are not applicable in graph transformation systems, proposing a backward graph transformation conflict detecting algorithm. At first the computation of conflict and dependency of two rules is available by use of AGG . Secondly the set of dependencies has to be tested by Warshall algorithm and the set of conflicts has to be computed by backward algorithm. At last, the termination of graph transformation systems and validity of rules can be detected as well.

This paper shows how integrated UML models combining class, object, use-case, collaboration and state diagrams can be animated in a domain-specific layout. The presented approach is based on graph transformation, i.e., UML model diagrams are translated to a graph transformation system and the behavior of the integrated model is simulated by applications of graph transformation rules. For model validation, users may prefer to see the behavior of selected model aspects as scenarios presented in the layout of the application domain. We propose to integrate animation views with the model's graph transformation system. A prototypical validation system has been implemented recently supporting the automatic translation of a UML model into a graph transformation system, and the interactive execution and simulation of the model behavior. We sketch the tool interconnection to GenGED, a visual language environment which allows to enrich graph transformation systems for model simulation by features for animation.

The algebraic graph transformation approach was initiated in 1973 and supports the rule-based modification of graphs based on pushout constructions. The vertex and edge types used within the rules (or productions) as well as possible inheritance relationships defined between them are specified in the type graph. However, the termination proof can only be accomplished for graph transformation systems without inheritance relationships. Thus, all graph transformation systems with inheritance relationships in the type graph must be flattened. To this end, the algebraic graph transformation approach provides a formal description for how to flatten the type graph as well as a definition of abstract and concrete productions. In this paper, we will extend the definitions to also consider vertices in negative application conditions with finer node types and positive application conditions. Furthermore, we will prove the semantic equivalence of the original and the flattened graph transformation system. The whole flattening algorithm is then implemented in a prototype which supports an abstract or concrete flattening of a given graph transformation system. The prototype is finally evaluated within a case study.

A structural approach to graph transformation based on symmetric Petri nets

Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of their computational properties. The aim of this chapter is to review and compare various concurrent semantics for the double pushout (DPO) algebraic approach to graph transformation, using different mathematical structures and describing computations at different levels of abstraction. We first present a trace semantics, based on the classical shift equivalence on graph derivations. Next we introduce graph processes, which lift to the graph transformation framework the notion of non-sequential process for Petri nets. Trace and process semantics are shown to be equivalent, in the sense that given a graph transformation system, the corresponding category of derivation traces and that of (concatenable) processes turns out to be isomorphic. Finally, a more abstract description of graph transformation systems computations is given by defining a semantics based on Winskel’s event structures.

Efficient Detection of Conflicts in Graph-based Model Transformation

Model-based test suite generation for graph transformation system using model simulation and search-based techniques