Graph Tuple Transformation

Graph transformation units are rule-based devices to model and compute relations between initial and terminal graphs. In this paper, they are generalized to graph tuple transformation units that allow one to combine different kinds of graphs into tuples and to process the component graphs simultaneously and interrelated with each other. Moreover, one may choose some of the working components as inputs and some as outputs such that a graph tuple transformation unit computes a relation between input and output tuples of potentially different kinds of graphs rather than a binary relation on a single kind of graphs

GRACE as a unifying approach to graph-transformation-based specification1 1This work was partially supported by the ESPRIT Working Group Applications of Graph Transformation (APPLIGRAPH) and the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems).

AbstractIn this paper, we sketch some basic ideas and features of the graph-transformation-based specification language GRACE. The aim of GRACE is to support the modeling of a wide spectrum of graph and graphical processes in a structured and uniform way including visualization and verification

Layered Fixed Point Logic

We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive specifications of properties. Two main theoretical contributions are a Moore Family result and a parametrized worst case time complexity result. We show that the logic and the associated solver can be used for rapid prototyping and illustrate a wide variety of applications within Static Analysis, Constraint Satisfaction Problems and Model Checking. In all cases the complexity result specializes to the worst case time complexity of the classical methods

Graph Transformation Model of a Triangulated Network of Mobile Units

A triangulated network of mobile units is modelled by means of a graph trans-formation system in which graph nodes are labelled with geometric coordinates and edges are labelled with distances. Nodes represent mobile units and edges represent wireless radio communication links between them. Under concurrency the model can describe interesting practical scenarios, for example swarms of taxis in an urban environment. The contribution features the enhancement of a graph transformation system by trigonometric calculations. By the way it is also shown that the classical negative edge condition has only limited applicability if a strict locality principle is assumed, and "vice versa" that there are reasonable modeling cases in which this locality principle itself fails to suffice

Modelling and Analysis Using GROOVE

In this paper we present case studies that describe how the graph transformation tool GROOVE has been used to model problems from a wide variety of domains. These case studies highlight the wide applicability of GROOVE in particular, and of graph transformation in general. They also give concrete templates for using GROOVE in practice. Furthermore, we use the case studies to analyse the main strong and weak points of GROOVE

Interleaving and lock-step semantics for analysis and verification of GPU kernels

Graphics Processing Units (GPUs) from leading vendors employ predicated (or guarded) execution to eliminate branching and increase performance. Similarly, a recent GPU verification technique uses predication to reduce verification of GPU kernels (the massively parallel programs that run on GPUs) to verification of a sequential program. Prior work on the formal semantics of lock-step predicated execution for kernels focused on structured programs, where control is organised using if- and while-statements. We provide lock-step execution semantics for GPU kernels that are represented by arbitrary reducible control flow graphs. We present a traditional interleaving semantics and a novel lock-step semantics based on predication, and show that for terminating kernels either both semantics compute identical results or both behave erroneously. The method allows reducing GPU kernel verification to the verification of a sequential, lock-step program to be applied to GPU kernels with arbitrary reducible control flow. We have implemented the method in the GPUVerify tool, and present an evaluation using a set of 163 open source and commercial GPU kernels. Among these kernels, 42 exhibit unstructured control flow which our novel lock-step predication technique can handle fully automatically. This generality comes at a modest price: verification across our benchmark set was on average 2.25 times slower than using an existing approach that specifically targets structured kernels

Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430