Optimization in Graph Transformation Systems Using Petri Net Based Techniques

On translating UML models into graph transformation systems

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.

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.

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.

Philosophy regarding the design of production systems

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.

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

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.

Scenario-driven analysis of systems specified through graph transformations

Combining economic and social goals in the design of production systems by using ergonomics standards

Microwave breast hyperthermia is a noninvasive treatment method for breast cancer that utilizes microwave energy (ME) sources to raise tissue temperatures above 42 , inducing tumor cell necrosis. The efficiency of ME deposition depends on the electric field magnitude and tissue conductivity, with antenna phase and amplitude adjustments used to maximize the electric field magnitude within tumors. Achieving precise ME focusing in the complex and heterogeneous breast tissue is challenging and can lead to unwanted hot spots in normal tissue. This study presents a novel method for optimizing ME focusing on the center of target tumors, using a simplified calculation of antenna phases, heuristic optimization for antenna amplitudes, and realistic breast phantoms for performance evaluation. In this work, we propose an approach to optimize the microwave hyperthermia system, employing phase and amplitude modulation techniques to concentrate the electric field at the center of a malignant tumor within a breast medium. The approach uses line sources arranged in a circular pattern around realistic breast models. The method begins by determining the phase, followed by adjusting the amplitudes of each source in order to maximize the total electric field at the tumor's center. The goal is to maximize the electric field at the tumor center while minimizing the optimization cost andcomplexity. Simulations are performed at 4 GHz frequency using two different types of digital breast phantoms (fatty and dense breasts) as test beds. The algorithm is tested by using three quantities; that is, the electric field distribution, the power density distribution, and the temperature distribution inside the whole breast region. The electric field and power density are calculated using an in-house method of moments (MoM) algorithm, while the temperature distributions are obtained with computer simulation technology (CST) software. To further evaluate the method with quantitative measures of success, thermal indices are calculated for each phantom andmethod. The specific absorbtion rate (SAR) results and corresponding temperature distributions for each breast type and optimization demonstrate that effective focusing is achieved in both cases. However, the combined phase-amplitude optimization provides more precise focusing by eliminating hot spots. Among thermal indices, the TC75 and T90 values obtained from the phase-amplitude combined optimization for both breast types outperform the results found in the literature. The T50 values obtained using the combined optimization are above 42 . This study presents an optimization method for focusing ME within breast tissue, performed in two steps: first phase optimization, followed by amplitude optimization. The electric field calculations are performed using both the MoM and Finite Difference Time Domain methods. The technique is numerically tested on two realistic breast models, with thermal indices calculated for each phantom and optimization process. Results show T90 values exceeding 40 and T50 values above 42 . While the study employs a 2D applicator, it provides a strong foundation for future development in 3Dapplications.

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.