Symmetry for the Analysis of Dynamic Systems

On translating UML models into graph transformation systems

Scenario-driven analysis of systems specified through graph transformations

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.

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.

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 \(\mathcal {R}\).

A heuristic solution for model checking graph transformation systems

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.

Non-functional requirements like performance and reliability play a prominent role in distributed and dynamic systems. To measure and predict such properties using stochastic formal methods is crucial. At the same time, graph transformation systems are a suitable formalism to formally model distributed and dynamic systems. Already, to address these two issues, Stochastic Graph Transformation Systems (SGTS) have been introduced to model dynamic distributed systems. But most of the researches so far are concentrated on SGTS as a modeling means without considering the need for suitable analysis tools. In this paper, we present an approach to verify this kind of graph transformation systems using PRISM (a stochastic model checker). We translate the SGTS to the input language of PRISM and then PRISM performs the model checking and returns the results back to the designers.

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

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.

Stochastic graph transformation systems (SGTS) [1] support integrated modelling of architectural reconfiguration and non-functional aspects such as performance and reliability. In its simplest form a SGTS is a graph transformation system (GTS) where each rule name is associated with a rate of an exponential distribution governing the delay of its application. However, this approach has its limitations. Model checking with explicit states does not scale well to models with large state space. Since performance and reliability properties often depend on the behaviour of large populations of entities (network nodes, processes, services, etc.), this limitation is significant. Also, exponential distributions do not always provide the best abstraction. For example, the time it takes to make a phone call or transmit a message is more likely to follow a normal distribution.

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.

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.

One motivation for software models is the ability to analyse them, for example to validate requirements and verify the consistency of models with each other or with respect to an implementation. Since we want to use graph transformation systems as software engineering models, we have to provide analysis techniques to answer questions about these systems that arise in their applications to software engineering problems.

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.