Warshall Based Detection of Conflicts and Dependencies in Graph Transformation System

In this paper a graph transformation system with the parallel derivation is used to model the process of distribution and adaptation for computer aided design. It is based on earlier research in formal language theory, especially graph grammars, and distributed models. The motivation for the ideas presented here is given and possible ways of application are described. A connection to the multi-agent model is also presented.

On translating UML models into graph transformation systems

In this work we show that the reachability problem for graph transformation systems is in the complexity class XP when parameterized with respect to the depth of derivations and the cutwidth of the source graph. More precisely, we show that for any set \(\mathcal {R}\) of graph transformation rules, one can determine in time \(f(c,d)\cdot |G|\cdot |H|^{g(c,d)}\) whether a graph G of cutwidth c can be transformed into a graph H in depth at most d by the application of graph transformation rules from \(\mathcal {R}\). In particular, our algorithm runs in polynomial time when c and d are constants. On the other hand, we show that the problem becomes NP-hard if we allow \(c=O(|G|)\) and \(d=5\). In the case in which all transformation rules are monotone we get an algorithm running in time \(f(c,d)\cdot |G|^{O(c)}\cdot |H|\). To prove our main theorems we will establish an interesting connection between graph transformation systems and regular slice languages. More precisely, we show that if \(\mathcal {A}\) is a slice automaton representing a set \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) of graphs, then one can construct in time linear in \(|\mathcal {A}|\) a slice automaton \(\mathcal {N}(\mathcal {A})\) representing the set of all graphs that can be obtained from graphs in \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) by the application of one layer of transformation rules in \(\mathcal {R}\).

UML state machines are quite popular and useful to specify dynamic components of software systems. They have a formal static semantics but their execution semantics is described only informally. Graph transformation, on the other hand, constitutes a well-studied area with many theoretical results and practical application domains. In this paper, an operational semantics for a subset of UML state machines is proposed which is based on graph transformation. In more detail, a UML state machine is described as a structured graph transformation system in such a way that the wellformedness rules of UML state machines are satisfied and the firing of a (maximum) set of enabled non-conflicting transitions corresponds to the application of a graph transformation rule. The presented approach uses the concept of transformation units, a recently developed modularization concept for graph transformation systems.

A rich concurrent semantics has been developed along the years for graph transformation systems, often generalizing in non-trivial ways concepts and results fist introduced for Petri nets. Besides the theoretical elegance, the concurrent semantic has potential applications in verification, e.g. in partial order reduction or in the use of finite prefixes of the unfolding for model checking. In practice (graph) transformation systems are often equipped with Negative Application Conditions, that describe forbidden contexts for the application of a rule. The talk will summarize some recent results showing that if the NACs are sufficiently simple (“incremental”) the concurrent semantics lifts smoothly to systems with NACs, but the general case requires original definitions and intuitions. Joint work with Reiko Heckel, Frank Hermann, Susann Gottmann and Nico Nachtigall

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.

Model checking is one of the successful techniques in automated verification of software and hardware systems. However, employing this technique for verification of properties such as the safety and liveness requires that all possible states of a system are generated and then the given property is checked. In large and complex systems, generating all states causes the state space explosion problem. Hence, it is possible to refute such properties by searching the state space to find a state in which the given property is violated. Of course, it is possible that detecting such states in complex systems leads to the exhaustive exploration of the state space. Recent researches confirm that using meta-heuristic and evolutionary approaches to intelligently explore a portion of the state space can be a promising idea. Hence, in this paper, we propose an approach based on ant colony optimization algorithm for refuting the safety and liveness properties and also analyzing reachability ones in systems specified formally through graph transformation system. Refutation of liveness and analyzing reachability properties in systems modeled by graph transformations are the prominent advantages of this approach in comparison with the previous approaches. The proposed approach is implemented in GROOVE which is an open source toolset for designing and model checking graph transformation systems. Experimental results show that our proposed approach is faster and it generates shorter counterexamples in comparison with others.

Scenario-driven analysis of systems specified through graph transformations

The design of business or production systems frequently necessitates to simultaneously fulfill several logical and numerical constraints as requirements in order to deliver a functionally correct and optimal system. Such a problem can be typically formulated as a combined optimization and reachability analysis. In the current paper, we show how this problem can be formalized when the evolution of the system is captured by graph transformation systems (GTS) with a cost parameter attached to each graph transformation rule denoting the cost of firing the rule. Furthermore, we discuss how to solve such problems by combining guided state space exploration with algebraic techniques of Petri nets.

In the framework of graph transformation systems with Negative Application Conditions (NACs) the classical notion of switch equivalence of derivations is extended to permutation equivalence, because there are intuitively equivalent derivations which are not switch-equivalent if NACs are considered. By definition, two derivations are permutation-equivalent, if they respect the NACs and disregarding the NACs they are switch equivalent. A direct analysis of permutation equivalence is very complex in general, thus we propose a much more efficient analysis technique. For this purpose, we construct a Place/Transition Petri net, called dependency net, which encodes the dependencies among rule applications of the derivation, including the inhibiting effects of the NACs. The analysis of permutation equivalence is important for analysing simulation runs within development environments for systems modelled by graph transformation. The application of the technique is demonstrated by a graph transformation system within the context of workflow modelling. We show the effectiveness of the approach by comparing the minimal costs of a direct analysis with the costs of the efficient analysis applied to a derivation of our example system.

Grammar inference deals with determining (preferably simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly little known on grammar inference for graph grammars. In this article, we take a further step in this direction and work within the framework of node label controlled (NLC) graph grammars. Specifically, given a graph G and a set 𝒮 of disjoint and isomorphic subgraphs of G, we characterize whether or not there is a graph grammar consisting of one production such that G may be derived from G0, the graph obtained from G by ‘contraction’ of each subgraph in 𝒮 to a node labelled by N. This generalizes a previous result that assumes boundary NLC graph grammars, and leads one to consider the more involved ‘non-confluent’ graph grammar rules.

In this paper we give graph-semantics to a fundamental part of the semantics of the service modeling language SRML: business configurations. To achieve this goal we use symbolic graph transformation systems. We formalize the semantics using this graph transformation system and illustrating it with a simple running example of a trip booking agent.

This paper proposes a methodology to analyze graph transformation systems by means of Alloy and its supporting tools. Alloy is a simple structural modeling language, based on first-order logic, that allows the user to produce models of software systems by abstracting their key characteristics. The tools can generate instances of invariants, and check properties of models, on user-constrained representations of the world under analysis. The paper describes how to render a graph transformation system —specified using AGG— as an Alloy model and how to exploit its tools to prove significant properties of the system. Specifically, it allows the user to decide whether a given configuration (graph) can be obtained through a finite and bounded sequence of steps (invocation of rules), whether a given sequence of rules can be applied on an initial graph, and, given an initial graph and an integer n, which are the configurations that can be obtained by applying a sequence of n (particular) rules.

The paper presents a conceptual framework for a module concept for graph transformation systems from a software engineering as well as from a theoretical point of view. The basic idea is to reuse concepts, which are known within or without the graph grammar field, to structure large specifications. These are the concept of distributed graph transformation systems, the concept of inheritance of specifications, and the import-export-interface concept. All these concepts are presented in a uniform framework based on the syntactical notion of a graph class specification and its semantics given by a graph transformation system. This is the basis for an explicit integration of these concepts and a corresponding specification language, to be discussed in a subsequent paper.

Agent systems demand from graph transformation systems not only an effectiveness of parsing but also supporting of the online derivation control (in order to visualize or control of their development). The way of the effective realization Derivation Control Environment for the distributed systems is presented. Finally, the computational effectiveness of the parsing, membership problems of the full graph transformation system is discussed.