Algebraic Graph Transformation Research Articles

A Survey on Syntactic Pattern Recognition Methods in Bioinformatics

Formal tools and models of syntactic pattern recognition which are used in bioinformatics are introduced and characterized in the paper. They include, among others: stochastic (string) grammars and automata, hidden Markov models, programmed grammars, attributed grammars, stochastic tree grammars, Tree Adjoining Grammars (TAGs), algebraic dynamic programming, NLC- and NCE-type graph grammars, and algebraic graph transformation systems. The survey of applications of these formal tools and models in bioinformatics is presented.

Comprehensive Systems: A formal foundation for Multi-Model Consistency Management

Model management is a central activity in Software Engineering. The most challenging aspect of model management is to keep inter-related models consistent with each other while they evolve. As a consequence, there is a lot of scientific activity in this area, which has produced an extensive body of knowledge, methods, results and tools. The majority of these approaches, however, are limited to binary inter-model relations; i.e. the synchronisation of exactly two models. Yet, not every multi-ary relation can be factored into a family of binary relations. In this paper, we propose and investigate a novel comprehensive system construction, which is able to represent multi-ary relations among multiple models in an integrated manner and thus serves as a formal foundation for artefacts used in consistency management activities involving multiple models. The construction is based on the definition of partial commonalities among a set of models using the same language, which is used to denote the (local) models. The main theoretical results of this paper are proofs of the facts that comprehensive systems are an admissible environment for (i) applying formal means of consistency verification (diagrammatic predicate framework), (ii) performing algebraic graph transformation (weak adhesive HLR category), and (iii) that they generalise the underlying setting of graph diagrams and triple graph grammars.

An Algebraic Graph Transformation Approach for RDF and SPARQL

We consider the recommendations of the World Wide Web Consortium (W3C) about RDF framework and its associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We define RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

On the essence and initiality of conflicts in [formula omitted]-adhesive transformation systems

Understanding conflicts between transformation steps and rules is an important topic in algebraic graph transformation. A conflict occurs when two transformation steps are not parallel independent, that is, when after applying one of them the other can no longer occur. A static analysis technique called Critical Pair Analysis allows the detection of all potential conflicts between pairs of rules, by enumerating Critical Pairs. Since these are often too numerous for even simple rules, finding appropriate subsets of critical pairs is the topic of ongoing research. We contribute to this thread by proposing a new characterization for root causes of conflicts, called “conflict essences”, exploiting a recently proposed characterization of parallel independence. Furthermore we show that conflict essences are at least as precise as the “conflict reasons” previously proposed, and uniquely determine the so-called “initial conflicts”, an appropriate subset of critical pairs, under relatively mild assumptions on the underlying category. Finally, we show that several M-adhesive categories of interest have the necessary properties for our results to hold, including typed, attributed and symbolic graphs. While our results are formulated for conflicts, they are directly applicable to dependencies in M-adhesive transformation systems.

A technique to validate automatic generation of Büchi automata from UML 2 sequence diagrams based on multi layer transformations

Several approaches have been proposed in the literature to transform UML models to formal methods for verification reason. However, few of these approaches take into account the validation of such transformations. This paper is a proposal in this context. It has two parts; first, we propose a technique to control the output of a transformational tool, in order to obtain safe transformational rules, and second, we propose a way to generate the formal model Büchi automata. More particularly, we show how to use multi layer transformations to obtain Büchi automata From UML2SD. The validation technique is based on the algebraic graph transformations and on the use of AGG tool. A scenario of telephone system is taken as a case study to illustrate our validation technique.

A technique to validate automatic generation of Büchi automata from UML 2 sequence diagrams based on multi layer transformations

Several approaches have been proposed in the literature to transform UML models to formal methods for verification reason. However, few of these approaches take into account the validation of such transformations. This paper is a proposal in this context. It has two parts; first, we propose a technique to control the output of a transformational tool, in order to obtain safe transformational rules, and second, we propose a way to generate the formal model Buchi automata. More particularly, we show how to use multi layer transformations to obtain Buchi automata From UML2SD. The validation technique is based on the algebraic graph transformations and on the use of AGG tool. A scenario of telephone system is taken as a case study to illustrate our validation technique.

Translation of ATL to AGT and application to a code generator for Simulink

Analysing and reasoning on model transformations has become very relevant for various applications such as ensuring the correctness of transformations. ATL is a model transformation language with rich semantics and a focus on usability, making its analysis not straightforward. Conversely, algebraic graph transformation (AGT) is an approach with strong theoretical foundations allowing for formal analyses that would be valuable in the context of ATL. In this paper, we propose a translation of ATL to the AGT framework in the objective of bringing theoretical analyses of AGT to ATL transformations. We show that this transformation supports a sufficient subset of ATL to be used on an industrial application example: QGen, a qualifiable Simulink\(^{\circledR }\) to source code generator developed at AdaCore. In addition to this example, we validate our proposal by translating a set of feature-rich ATL transformations to the Henshin AGT framework. We execute the ATL and AGT versions on the same set of models and verify that the result is the same.

On A Graph Formalism for Ordered Edges

Though graphs are flexible enough to model any kind of data structure in principle, for some structures this results in a rather large overhead. This is for instance true for lists, i.e., edges that are meant to point to an ordered collection of nodes. Such structures are frequently encountered, for instance as ordered associations in UML diagrams. Several options exist to model lists using standard graphs, but all of them need auxiliary structure, and even so their manipulation in graph transformation rules is not trivial. In this paper we propose to enrich graphs with special ordered edges, which more naturally represent the intended structure, and define how lists can be manipulated. We show that the resulting category satisfies sufficient HLR properties to apply standard algebraic graph transformation. We believe that in a context where lists are common, the cost of a more complicated graph formalism is outweighed by the benefit of a smaller, more appropriate model and more straightforward manipulation.

Multi-amalgamated triple graph grammars: Formal foundation and application to visual language translation

Visual languages (VLs) facilitate software development by not only supporting communication and abstraction, but also by generating various artifacts such as code and reports from the same high-level specification. VLs are thus often translated to other formalisms, in most cases with bidirectionality as a crucial requirement to, e.g., support re-engineering of software systems. Triple Graph Grammars (TGGs) are a rule-based language to specify consistency relations between two (visual) languages from which bidirectional translators are automatically derived. TGGs are formally founded but are also limited in expressiveness, i.e., not all types of consistency can be specified with TGGs. In particular, 1-to-n correspondence between elements depending on concrete input models cannot be described. In other words, a universal quantifier over certain parts of a TGG rule is missing to generalize consistency to arbitrary size. To overcome this, we transfer the well-known multi-amalgamation concept from algebraic graph transformation to TGGs, allowing us to mark certain parts of rules as repeated depending on the translation context. Our main contribution is to derive TGG-based translators that comply with this extension. Furthermore, we identify bad smells on the usage of multi-amalgamation in TGGs, prove that multi-amalgamation increases the expressiveness of TGGs, and evaluate our tool support.

Algebraic graph transformations with inheritance and abstraction

In this paper, we propose a new approach to inheritance and abstraction in the context of algebraic graph transformation by providing a suitable categorial framework which reflects the semantics of class-based inheritance in software engineering. Inheritance is modelled by a type graph T that comes equipped with a partial order. Typed graphs are arrows with codomain T which preserve graph structures up to inheritance. Morphisms between typed graphs are “down typing” graph morphisms: An object of class t can be mapped to an object of a subclass of t. Abstract classes are modelled by a subset of vertices of the type graph. We prove that this structure is an adhesive HLR category, i.e. pushouts along extremal monomorphisms are “well-behaved”. This infers validity of classical results such as the Local Church–Rosser Theorem, the Parallelism Theorem, and the Concurrency Theorem.

An Operational Semantics for UML 2 Sequence Diagrams Supported by Model Transformations

Abstract In this paper, we propose an operational semantics for UML2SD (Unified Modeling Language 2 Sequence Diagrams) to its equivalent Buchi automaton. The objective of this paper is twofold; first we provide UML2SD with Buchi automaton formal semantics, and second we bridge the gap between theoretic studies to practical studies by improving model transformations. The approach is based on Algebraic graph transformation and uses AGG (Attribut Graph Grammar) tool. The rules of the graph grammars specifying transformation of basic interactions and combined fragments are based on the proposed semantics. A scenario of ATM (Automatic Teller Machine) as case study will illustrate our approach.

Algebraic graph transformations for formalizing ontology changes and evolving ontologies

An ontology represents a consensus on the representation of the concepts and axioms of a given domain. This consensus is often reached through an iterative process, each iteration consisting in modifying the current version of the consensus. Furthermore, frequent and continuous changes are also occurring when the represented domain evolves or when new requirements have to be considered. Consequently, ontologies have to be adaptable to handle evolution, revision and refinement. However, this process is highly challenging as it is often difficult to understand all affected ontology parts when changes are performed. Thus, inconsistencies can occur in the ontology as the changes can introduce contradictory axioms. To address this issue, this paper presents a formal approach for evolving ontologies using Typed Graph Grammars. This method relies on the algebraic approach Simple PushOut (SPO) of graph transformations. It formalizes the ontology changes and proposes an a priori approach of inconsistencies resolution. The modified ontology does not need an explicit checking as an incorrect ontology version cannot actually be generated. To validate our proposal, an implementation is presented using the Attributed Graph Grammar (AGG) toolbox.

Towards “mouldable code” via nested code graph transformation

Program transformation is currently de facto restricted to abstract syntax tree rewriting. However, many program transformation patterns, in particular in the realm of high-performance code generation, can more naturally be understood and expressed as graph transformations. We describe the conceptual organisation of a system based on application of algebraic graph transformation rules to data-flow and control-flow graphs, and outline the work, both theoretical and of implementation nature, that still needs to be done to realise this long-term project.

Deontic BPMN: a powerful extension of BPMN with a trusted model transformation

The Business Process Model and Notation (BPMN) is a widely-used standard for process modelling. A drawback of BPMN, however, is that modality is implicitly expressed through the structure of the process flow but not directly within the corresponding activity. Thus, an extension of BPMN with deontic logic has been proposed in previous work, called Deontic BPMN. Deontic BPMN reduces the structural complexity of the process flow and increases the readability by explicitly highlighting obligatory and permissible activities. In addition, an algebraic graph transformation from a subset of BPMN to Deontic BPMN, called Deontic BpmnGTS, has been defined. The goal of the current research is to show that DeonticBpmnGTS is terminating and confluent, resulting in a globally deterministic transformation. Moreover, the semantic equivalence of BPMN models and the respective Deontic BPMN models is proven based on Abstract State Machines (ASMs). Thus, DeonticBpmnGTS can be called a trusted model transformation.

A framework for families of domain-specific modelling languages

Domain-specific modelling langugages, which are tailored to the requirements of their users, can significantly increase the acceptance of formal (or at least semi-formal) modelling in scenarios where informal diagrams and natural language descriptions are predominant today. We show in this article how the Resource Description Framework (RDF), which is a standard for the fundamental data structures of the Semantic Web, and algebraic graph transformations on these data structures can be used to realise and modify the abstract syntax of models in such domain-specific languages. We examine a small domain-specific modelling language for IT infrastructures--inspired by real-world requirements from a banking environment--as an application scenario. From this scenario, we derive four key requirements for a domain-specific modelling framework: (1) distributed modelling, (2) evolution of language definitions, (3) migration of legacy models and (4) integration of modelling languages. RDF and transformation rules are then used to provide a solution which meets these requirements simultaneously, where all kinds of modifications--from simple editing steps via model migration to language integration--are realised in an integrated manner by the single, declarative formalism of algebraic graph transformation.

On formalizing EMF modeling operations with graph transformations

The development of software in accordance with the model-driven engineering paradigm places model transformations at a central position. Desirable yet contradicting properties of model transformations are user-friendliness as offered by-demonstration approaches and formal conciseness as provided by algebraic graph transformations which is indispensable for verification tasks. In this paper, we show how to unite the properties of the two different approaches. We employ the state-of-the-art by-demonstration environment Emo to prototype graph transformations by embedding the operations obtained from Emo in the formal framework of graph transformation theory.

Collagories: Relation-algebraic reasoning for gluing constructions

The relation-algebraic approach to graph transformation has previously been formalised in the context of complete distributive allegories. Careful analysis reveals that the zero laws postulated for distributive allegories were never used, and that completeness was most importantly used for the difunctional closures necessary for a relation-algebraic characterisation of pushouts. We therefore define collagories essentially as “distributive allegories without zero morphisms”, and also define a variant of Kleene star to produce difunctional closures where necessary. Typical collagories relevant for generalised graph structure transformation can be obtained from basic collagories like that of sets and relations via nestable constructions of collagories of semi-unary algebras, which allow natural representations in particular of graph structures, also with fixed label sets, or with type graphs. Since collagories are intended as foundation for generalised graph structure transformation in the algebraic tradition, we concentrate particularly on co-tabulations, the core of the relation-algebraic gluing concept. We clarify the precise relationship between co-tabulations and pushouts, and investigate the special case of direct sums, which is particularly affected by the absence of zero laws. Finally, we consider Van Kampen squares, the central ingredient of the definition of adhesive categories that has recently become popular as foundation for algebraic graph transformation, and obtain an interesting characterisation of Van Kampen squares in collagories.

Formal foundation of consistent EMF model transformations by algebraic graph transformation

Model transformation is one of the key activities in model-driven software development. An increasingly popular technology to define modeling languages is provided by the Eclipse Modeling Framework (EMF). Several EMF model transformation approaches have been developed, focusing on different transformation aspects. To validate model transformations with respect to functional behavior and correctness, a formal foundation is needed. In this paper, we define consistent EMF model transformations as a restricted class of typed graph transformations using node type inheritance. Containment constraints of EMF model transformations are translated to a special kind of graph transformation rules such that their application leads to consistent transformation results only. Thus, consistent EMF model transformations behave like algebraic graph transformations and the rich theory of algebraic graph transformation can be applied to these EMF model transformations to show functional behavior and correctness. Furthermore, we propose parallel graph transformation as a suitable framework for modeling EMF model transformations with multi-object structures. Rules extended by multi-object structures can specify a flexible number of recurring structures. The actual number of recurring structures is dependent on the application context of such a rule. We illustrate our approach by selected refactorings of simplified statechart models. Finally, we discuss the implementation of our concepts in a tool environment for EMF model transformations.

A collection operator for graph transformation

Algebraic graph transformation has a wellestablished theory and associated tools that can be used to perform model transformations. However, the lack of a construct to match and transform collections of similar subgraphs makes graph transformation complex or even impractical to use in a number of transformation cases. This is addressed in this paper, by defining a collection operator which is powerful, yet simple to model and understand. A rule can contain multiple collection operators, each with lower and upper bound cardinalities, and the collection operators can be nested. An associated matching process dynamically builds a collection free rule that enables us to reuse the existing graph transformation apparatus. We present model transformation examples from different modeling domains to illustrate the benefit of the approach.

How to delete categorically — Two pushout complement constructions

In category theory, most set-theoretic constructions–union, intersection, etc.–have direct categorical counterparts. But up to now, there is no direct construction of a deletion operation like the set-theoretic complement. In rule-based transformation systems, deletion of parts of a given object is one of the main tasks. In the double pushout approach to algebraic graph transformation, the construction of pushout complements is used in order to locally delete structures from graphs. But in general categories, even if they have pushouts, pushout complements do not necessarily exist or are unique. In this paper, two different constructions for pushout complements are given and compared. Both constructions are based on certain universal constructions in the sense of category theory. More specifically, one uses initial pushouts while the other one uses quasi-coproduct complements. These constructions are applied to examples in the categories of graphs and simple graphs.