Distributed Adaptive Design with Hierarchical Autonomous 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.

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.

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.

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.

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.

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

В цифровую эпоху в процессе автоматизации, роботизации различных отраслей производства и внедрения в него искусственного интеллекта используется уже трудно обозримое множество языков программирования. В результате в подготовке будущих инженеров все большое значение приобретает теория формальных языков, лежащая в основе разработки языков программирования. Незнание теории формальных языков стало причиной многих ошибок в разработке и использовании языков программирования в высокотехнологичных отраслях производства. Поэтому необходимо внедрение в содержание подготовки будущих инженеров дисциплины «Элементы теории формальных языков» для овладения ими теорией и практикой языков программирования. Установлено, что в методической литературе не разработаны эффективные методы обучения будущих инженеров формальным языкам. Цель статьи заключается в исследовании важных математических и методических аспектов обучения теории формальных языков будущих инженеров. Ведущую роль в исследовании играли методология дискретной математики и абстрактной алгебры, культурологический подход и методика преемственности в обучения между школой и вузом в содержании подготовки будущих инженеров. Результаты исследования. Охарактеризована культурологическая роль дискретной математики в современной теории формальных языков. На основе анализа избранных трудов В. М. Глушкова, Д. Кнута и других ученых исследована фундаментальная роль формальных языков абстрактной алгебры в обучении теории формальных языков. Охарактеризованы алгебраические аспекты методики обучения теории формальных языков и грамматик и роль в этой методике классических понятий абстрактной алгебры и их свойств. На основе этого изложены элементы методики преемственности в обучении элементам теории формальных языков будущих инженеров. В этих элементах важную роль играют различные трактовки понятия «язык» и примеры языков из математики и информатики. Раскрыта важная роль грамматик формальных языков в дальнейшем обучении этой теории. Результаты статьи имеют важное теоретическое и практическое значение в дальнейшем исследовании проблем методологии обучения будущих инженеров элементам теории формальных языков. Они представляют интерес для преподавателей, ведущих профессиональную подготовку студентов инженерных направлений в сфере автоматизации, роботизации отраслей производства и внедрения в него Искусственного интеллекта. In the digital era, in the process of automation, robotization of various industries and the introduction of Artificial Intelligence into it, numerous programming languages are widely applied. As a result, the theory of formal languages ​that underlies the development of programming languages is becoming increasingly important in the training of engineering students. The nescience of formal languages theory has caused many mistakes in the development and use of programming languages ​in high-tech industries. Therefore, it is necessary to introduce the discipline "Elements of the Theory of Formal Languages" into the content of the training of future engineers in order to master the theory and practice of programming languages. At the same time, it was established that the methodological literature hasn’t developed effective methods for teaching future engineers to formal languages. The purpose of the article is to investigate important mathematical and methodological aspects of teaching the theory of formal languages ​to engineering students. The leading role in the study was played by the methodology of discrete math and abstract algebra. Also, the cultural approach and the methodology of pre-graduation in training between school and university in the content of training future engineers. Findings.The cultural role of discrete mathematics in the modern theory of formal languages is determined in the article. Based on the analysis of selected works of V.M. Glushkov, D. Knut, and other scientists, the article investigates the fundamental role of formal languages ​of abstract algebra in teaching the theory of formal languages. Algebraic aspects of teaching methodology of the theory of formal languages ​and grammars, and the role in this methodology of classical concepts of abstract algebra and their propertieshave also become the subjects of the study. Basing on this, the elements of the methodology of continuity in teaching the elements of the theory of formal languages of future engineers are set out in the article. Various interpretations of the concept of "language" and examples of languages from mathematics, and computer science play an important role in these elements. The research also states the important role of grammars of formal languages in the further training of this theory. The findings of the research have important theoretical and practical significance in the further study of the issues of the methodology for teaching future engineers to the elements of the theory of formal languages. They are of interest to teachers conducting the professional training of engineering students in the field of automation, robotization of production industries, and the introduction of Artificial Intelligence into it.

The issue of ontology evolution and change management is inadequately addressed by available tools and algorithms, mostly due to the lack of suitable knowledge representation formalisms to deal with temporal abstract notations and the overreliance on human factors. Also most of the current approaches have been focused on changes within the internal structure of ontologies and interactions with other existing ontologies have been widely neglected. In our research, after revealing and classifying some of the common alterations in a number of popular biomedical ontologies, we present a novel agent-based framework, Represent, Legitimate and Reproduce (RLR), to semi-automatically manage the evolution of bio-ontologies, with emphasis on the FungalWeb Ontology, with minimal human intervention. RLR assists and guides ontology engineers through the change management process in general and aids in tracking and representing the changes, particularly through the use of category theory and hierarchical graph transformation.

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.

Scenario-driven analysis of systems specified through graph transformations

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.

Earlier research on product family design (PFD) often highlights isolated and successful empirical studies with a limited attempt to explore the modeling and design support issues surrounding this economically important class of engineering design problems. This paper proposes a graph rewriting system to organize product family data according to the underpinning logic and to model product derivation mechanisms for PFD. It represents the structural and behavioral aspects of product families as family graphs and related graph operations, respectively. The derivation of product variants becomes a graph rewriting process, in which family graphs are transformed to variant graphs by applying appropriate graph rewriting rules. The system is developed in the language of programmed graph rewriting systems or PROGRES, which supports the specification of hierarchical graph schema and parametric rewriting rules. A meta model is defined for family graphs to factor out those entities common to all product families. A generic model is defined to describe all specific entities relevant to particular families. An instance model describes all product variants for individual customer orders. A prototype of a graph-based PFD system for office chairs is also developed. The system can provide an interactive environment for customers to make choices among product offerings. It also facilitates design automation of product families and enhances interactions and negotiations among sales, design, and manufacturing.