Agnès Arnould

Test sequences generation from LUSTRE descriptions: GATEL

We describe a test sequence generation method from LUSTRE descriptions and its companion tool, GATEL. The LUSTRE language is declarative and describes synchronous data-flow computations. It is used for reactive control/command systems, mainly for electrical power production applications. Such critical applications require a high level of reliability. While this language benefits from powerful verification tools, there is still a demand for adequate testing techniques. The method and the tool described can be applied during unit and integration testing, according to a structural (glass box) or functional (black box) test selection strategy. The test generation tool uses some interpretation of the language constructs as boolean and integer interval constraints. Test sequence generation is automated using constraint logic programming techniques. The method and the tool are illustrated on an example extracted from an industrial case study.

Testing from algebraic specifications: test data set selection by unfolding axioms

This paper deals with test data set selection from algebraic specifications. Test data sets are generated from selection criteria which are usually defined to cover specification axioms. The unfolding selection criterion consists in covering the input domain of an operation using case analysis. The unfolding procedure can be iterated in order to split input domains of operations into finer subdomains. In this paper we propose to extend an unfolding procedure previously developed in [5, 19] that could only be performed on very low level, i.e. executable specifications. On the contrary, our new unfolding procedure can be applied to any positive conditional specification. We show that our unfolding procedure is sound (no test is added) and complete (no test is lost) with respect to the starting reference test data set.

Test selection criteria for quantifier-free first-order specifications

This paper deals with test case selection from axiomatic specifications whose axioms are quantifier-free first-order formulae. Test cases are modeled as ground formulae and any specification has an exhaustive test data set whose successful submission means correctness, provided that the software under verification can be modeled as a first-order structure over the same signature. As it has already been done for positive conditional equational specifications, we derive test cases from selection criteria based on axiom coverage. Our selection criteria allows us to select test cases by iteratively unfolding an initial target test purpose, given as a formula. The initial reference test set is iteratively split into successive subsets. Each subset of test cases is defined by constraints which are increasingly introduced by the unfolding procedure to ensure an appropriate matching between the current test purpose under unfolding and specification axioms. Our unfolding procedure is sound (no test is added) and complete (no test is lost) with respect to the starting test purpose. It is exemplified on a simple example.

Designing a Topological Modeler Kernel: A Rule-Based Approach

In this article, we present a rule-based language dedicated to topological operations and based on graph transformations. Generalized maps are described as a particular class of graphs determined by consistency constraints. Hence, topological operations over generalized maps can be specified using graph transformations. The rules we define are provided with syntactic criteria which ensure that graphs computed by applying rules on generalized maps are also generalized maps. We have developed a static analyzer of transformation rules which checks the syntactic criteria in order to ensure the preservation of generalized map consistency constraints. Based on this static analyzer, we have designed a rule-based prototype of a kernel of a topology-based modeler that is generic in dimension. Since adding a new topological operation can be reduced to write a graph transformation rule, we directly obtain an extensible prototype where handled topological objects satisfy built-in consistency. Moreover, first benchmarks show that our prototype is reasonably efficient compared to a reference implementation of 3D generalized maps which use a classical implementation style.

Graph Transformation for Topology Modelling

In this paper we present meta-rules to express an infinite class of semantically related graph transformation rules in the context of pure topological modelling with G-maps. Our proposal is motivated by the need of describing specific operations to be done on topological representations of objects in computer graphics, especially for simulation of complex structured systems where rearrangements of compartments are subject to change. We also define application of such meta-rules and prove that it preserves some necessary conditions for G-maps.

Topology-based abstraction of complex biological systems: application to the Golgi apparatus

Many complex cellular processes involve major changes in topology and geometry. We have developed a method using topology-based geometric modelling in which the edge labels of an n-dimensional generalized map (a subclass of graphs) represent the relations between neighbouring biological compartments. We illustrate our method using two topological models of the Golgi apparatus. These models can be animated using transformation rules, which depend on geometric and/or biochemical data and which modify both these data and the topology. Both models constitute plausible topological representations of the Golgi apparatus, but only the model based on a recent hypothesis about the Golgi apparatus is fully compatible with data from electron microscopy. Finally, we outline how our method may help biologists to choose between different hypotheses.

Jerboa: A Graph Transformation Library for Topology-Based Geometric Modeling

Many software systems have to deal with the representation and the manipulation of geometric objects: video games, CGI movie effects, computer-aided design, computer simulations... All these softwares are usually implemented with ad-hoc geometric modelers. In the paper, we present a library, called Jerboa, that allows to generate new modelers dedicated to any application domains. Jerboa is a topological-based modeler: geometric objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc.) with relevant data as their geometric shape. Unlike other modelers, modeling operations are not implemented in a low-level programming language, but implemented as particular graph transformation rules so they can be graphically edited as simple and concise rules. Moreover, Jerboa’s modeler editor is equipped with many static verification mechanisms that ensure that the generated modelers only handle consistent geometric objects.

Rule-based transformations for geometric modelling

The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc.) with relevant data as their geometric shape (position, curve, surface, etc.) or application dedicated data (e.g. molecule concentration level in a biological context). We propose to define topology-based geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topology-based geometric objects constitute a particular subclass of a category of labelled graphs in which nodes have multiple labels.

Geometric Modelling with CASL

This paper presents an experiment that demonstrates the feasibility of successfully applying CASL to design 3D geometric modelling software. It presents an abstract specification of a 3D geometric model, its basic constructive primitives together with the definition of the rounding high-level operation. A novel methodology for abstractly specifying geometric operations is also highlighted. It allows one to faithfully specify the requirements of this specific area and reveals new mathematical definitions of geometric operations. The key point is to introduce an inclusion notion between geometric objects, in such a way that the result of an operation is defined as the smallest or largest object satisfying some pertinent criteria. This work has been made easier by using different useful CASL features, like first-order logic, free types or structured specifications. Some assets of this specification are to be abstract, readable by researchers in geometric modelling and to simplify the programming process.

A general physical-topological framework using rule-based language for physical simulation

This paper presents a robust framework that combines a topological model (a generalized map or G-map) and a physical one to simulate deformable objects. The framework is general since it allows a general simulation of deformations (1) in different dimensions (2D or 3D), (2) with different types of meshes (triangular, rectangular, tetrahedral, hexahedral, and combinations of them...) and (3) physical models (mass/spring, linear FEM, co-rotational, mass/tensor). Any mechanical information is stored in the topological model and is used in combination with the neighboring relations to compute the equation of motions. To design this model, we have used JERBOA, a rule-based language relying on graph transformations to handle G-maps. This tool has been helpful to build and test different physical models in a little time.