Arnaud Gotlieb

Helge Spieker, Jørn Eirik Betten, Arnaud Gotlieb

Multiple machine learning models can achieve near-equivalent predictive performance on the same task, yet provide divergent feature-based explanations. This is called the Rashomon effect of (explainable) machine learning, and it raises the question of which explanations, if any, are trustworthy. We propose a framework based on metamorphic testing that assesses explanation faithfulness without requiring ground-truth labels by exploring attributed feature importance from post-hoc explanation methods. Five metamorphic relations formalize expected consistency properties between model behavior and feature attributions. We apply this general framework to two tabular regression datasets and two post-hoc explainers (SHAP and LIME) to demonstrate the approach. The framework offers a practical, model-agnostic tool for selecting accurate models with reliable and trustworthy explanations.

Dusica Marijan, Arnaud Gotlieb

Context: Research collaborations between software engineering industry and academia can provide significant benefits to both sides, including improved innovation capacity for industry, and real-world environment for motivating and validating research ideas. However, building scalable and effective research collaborations in software engineering is known to be challenging. While such challenges can be varied and many, in this paper we focus on the challenges of achieving participative knowledge creation supported by active dialog between industry and academia and continuous commitment to joint problem solving. Objective: This paper aims to understand what are the elements of a successful industry-academia collaboration that enable the culture of participative knowledge creation. Method: We conducted participant observation collecting qualitative data spanning 8 years of collaborative research between a software engineering research group on software V&V and the Norwegian IT sector. The collected data was analyzed and synthesized into a practical collaboration model, named the Certus Model. Results: The model is structured in seven phases, describing activities from setting up research projects to the exploitation of research results. As such, the Certus model advances other collaborations models from literature by delineating different phases covering the complete life cycle of participative research knowledge creation. Conclusion: The Certus model describes the elements of a research collaboration process between researchers and practitioners in software engineering, grounded on the principles of research knowledge co-creation and continuous commitment to joint problem solving. The model can be applied and tested in other contexts where it may be adapted to the local context through experimentation.

Dusica Marijan, Arnaud Gotlieb

Machine learning has become prevalent across a wide variety of applications. Unfortunately, machine learning has also shown to be susceptible to deception, leading to errors, and even fatal failures. This circumstance calls into question the widespread use of machine learning, especially in safety-critical applications, unless we are able to assure its correctness and trustworthiness properties. Software verification and testing are established technique for assuring such properties, for example by detecting errors. However, software testing challenges for machine learning are vast and profuse - yet critical to address. This summary talk discusses the current state-of-the-art of software testing for machine learning. More specifically, it discusses six key challenge areas for software testing of machine learning systems, examines current approaches to these challenges and highlights their limitations. The paper provides a research agenda with elaborated directions for making progress toward advancing the state-of-the-art on testing of machine learning.

Pierre Bernabé, Arnaud Gotlieb, Bruno Legeard et al.

In maritime traffic surveillance, detecting illegal activities, such as illegal fishing or transshipment of illicit products is a crucial task of the coastal administration. In the open sea, one has to rely on Automatic Identification System (AIS) message transmitted by on-board transponders, which are captured by surveillance satellites. However, insincere vessels often intentionally shut down their AIS transponders to hide illegal activities. In the open sea, it is very challenging to differentiate intentional AIS shutdowns from missing reception due to protocol limitations, bad weather conditions or restricting satellite positions. This paper presents a novel approach for the detection of abnormal AIS missing reception based on self-supervised deep learning techniques and transformer models. Using historical data, the trained model predicts if a message should be received in the upcoming minute or not. Afterwards, the model reports on detected anomalies by comparing the prediction with what actually happens. Our method can process AIS messages in real-time, in particular, more than 500 Millions AIS messages per month, corresponding to the trajectories of more than 60 000 ships. The method is evaluated on 1-year of real-world data coming from four Norwegian surveillance satellites. Using related research results, we validated our method by rediscovering already detected intentional AIS shutdowns.

Nassim Belmecheri, Arnaud Gotlieb, Nadjib Lazaar et al.

The future of automated driving (AD) is rooted in the development of robust, fair and explainable artificial intelligence methods. Upon request, automated vehicles must be able to explain their decisions to the driver and the car passengers, to the pedestrians and other vulnerable road users and potentially to external auditors in case of accidents. However, nowadays, most explainable methods still rely on quantitative analysis of the AD scene representations captured by multiple sensors. This paper proposes a novel representation of AD scenes, called Qualitative eXplainable Graph (QXG), dedicated to qualitative spatiotemporal reasoning of long-term scenes. The construction of this graph exploits the recent Qualitative Constraint Acquisition paradigm. Our experimental results on NuScenes, an open real-world multi-modal dataset, show that the qualitative eXplainable graph of an AD scene composed of 40 frames can be computed in real-time and light in space storage which makes it a potentially interesting tool for improved and more trustworthy perception and control processes in AD.

Helge Spieker, Nassim Belmecheri, Arnaud Gotlieb et al.

The prediction of human trajectories is important for planning in autonomous systems that act in the real world, e.g. automated driving or mobile robots. Human trajectory prediction is a noisy process, and no prediction does precisely match any future trajectory. It is therefore approached as a stochastic problem, where the goal is to minimise the error between the true and the predicted trajectory. In this work, we explore the application of metamorphic testing for human trajectory prediction. Metamorphic testing is designed to handle unclear or missing test oracles. It is well-designed for human trajectory prediction, where there is no clear criterion of correct or incorrect human behaviour. Metamorphic relations rely on transformations over source test cases and exploit invariants. A setting well-designed for human trajectory prediction where there are many symmetries of expected human behaviour under variations of the input, e.g. mirroring and rescaling of the input data. We discuss how metamorphic testing can be applied to stochastic human trajectory prediction and introduce the Wasserstein Violation Criterion to statistically assess whether a follow-up test case violates a label-preserving metamorphic relation.

Dennis Gross, Helge Spieker, Arnaud Gotlieb et al.

This paper presents an explainable machine learning (ML) approach for predicting surface roughness in milling. Utilizing a dataset from milling aluminum alloy 2017A, the study employs random forest regression models and feature importance techniques. The key contributions include developing ML models that accurately predict various roughness values and identifying redundant sensors, particularly those for measuring normal cutting force. Our experiments show that removing certain sensors can reduce costs without sacrificing predictive accuracy, highlighting the potential of explainable machine learning to improve cost-effectiveness in machining.

Dennis Gross, Helge Spieker, Arnaud Gotlieb

We introduce a tool for rigorous and automated verification of large language model (LLM)- based policies in memoryless sequential decision-making tasks. Given a Markov decision process (MDP) representing the sequential decision-making task, an LLM policy, and a safety requirement expressed as a PCTL formula, our approach incrementally constructs only the reachable portion of the MDP guided by the LLM's chosen actions. Each state is encoded as a natural language prompt, the LLM's response is parsed into an action, and reachable successor states by the policy are expanded. The resulting formal model is checked with Storm to determine whether the policy satisfies the specified safety property. In experiments on standard grid world benchmarks, we show that open source LLMs accessed via Ollama can be verified when deterministically seeded, but generally underperform deep reinforcement learning baselines. Our tool natively integrates with Ollama and supports PRISM-specified tasks, enabling continuous benchmarking in user-specified sequential decision-making tasks and laying a practical foundation for formally verifying increasingly capable LLMs.

Arnaud Gotlieb, Dusica Marijan, Helge Spieker

Constraint Programming (CP) is a powerful declarative programming paradigm where inference and search are interleaved to find feasible and optimal solutions to various type of constraint systems. However, handling logical connectors with constructive information in CP is notoriously difficult. This paper presents If Then Else (ITE), a lightweight implementation of stratified constructive reasoning for logical connectives. Stratification is introduced to cope with the risk of combinatorial explosion of constructing information from nested and combined logical operators. ITE is an open-source library built on top of SICStus Prolog clp(fd), which proposes various operators, including constructive disjunction and negation, constructive implication and conditional. These operators can be used to express global constraints and to benefit from constructive reasoning for more domain pruning during constraint filtering. Even though ITE is not competitive with specialized filtering algorithms available in some global constraints implementations, its expressiveness allows users to easily define well-tuned constraints with powerful deduction capabilities. Our extended experimental results show that ITE is more efficient than available generic approaches that handle logical constraint systems over finite domains.

Helge Spieker, Théo Matricon, Nassim Belmecheri et al.

Software systems usually provide numerous configuration options that can affect performance metrics such as execution time, memory usage, binary size, or bitrate. On the one hand, making informed decisions is challenging and requires domain expertise in options and their combinations. On the other hand, machine learning techniques can search vast configuration spaces, but with a high computational cost, since concrete executions of numerous configurations are required. In this exploratory study, we investigate whether large language models (LLMs) can assist in performance-oriented software configuration through prompts. We evaluate several LLMs on tasks including identifying relevant options, ranking configurations, and recommending performant configurations across various configurable systems, such as compilers, video encoders, and SAT solvers. Our preliminary results reveal both positive abilities and notable limitations: depending on the task and systems, LLMs can well align with expert knowledge, whereas hallucinations or superficial reasoning can emerge in other cases. These findings represent a first step toward systematic evaluations and the design of LLM-based solutions to assist with software configuration.

Dennis Gross, Helge Spieker, Arnaud Gotlieb et al.

This research presents a method that utilizes explainability techniques to amplify the performance of machine learning (ML) models in forecasting the quality of milling processes, as demonstrated in this paper through a manufacturing use case. The methodology entails the initial training of ML models, followed by a fine-tuning phase where irrelevant features identified through explainability methods are eliminated. This procedural refinement results in performance enhancements, paving the way for potential reductions in manufacturing costs and a better understanding of the trained ML models. This study highlights the usefulness of explainability techniques in both explaining and optimizing predictive models in the manufacturing realm.

Nassim Belmecheri, Arnaud Gotlieb, Nadjib Lazaar et al.

This paper investigates the integration of graph neural networks (GNNs) with Qualitative Explainable Graphs (QXGs) for scene understanding in automated driving. Scene understanding is the basis for any further reactive or proactive decision-making. Scene understanding and related reasoning is inherently an explanation task: why is another traffic participant doing something, what or who caused their actions? While previous work demonstrated QXGs' effectiveness using shallow machine learning models, these approaches were limited to analysing single relation chains between object pairs, disregarding the broader scene context. We propose a novel GNN architecture that processes entire graph structures to identify relevant objects in traffic scenes. We evaluate our method on the nuScenes dataset enriched with DriveLM's human-annotated relevance labels. Experimental results show that our GNN-based approach achieves superior performance compared to baseline methods. The model effectively handles the inherent class imbalance in relevant object identification tasks while considering the complete spatial-temporal relationships between all objects in the scene. Our work demonstrates the potential of combining qualitative representations with deep learning approaches for explainable scene understanding in autonomous driving systems.

Nassim Belmecheri, Arnaud Gotlieb, Nadjib Lazaar et al.

Understanding driving scenes and communicating automated vehicle decisions are key requirements for trustworthy automated driving. In this article, we introduce the Qualitative Explainable Graph (QXG), which is a unified symbolic and qualitative representation for scene understanding in urban mobility. The QXG enables interpreting an automated vehicle's environment using sensor data and machine learning models. It utilizes spatio-temporal graphs and qualitative constraints to extract scene semantics from raw sensor inputs, such as LiDAR and camera data, offering an interpretable scene model. A QXG can be incrementally constructed in real-time, making it a versatile tool for in-vehicle explanations across various sensor types. Our research showcases the potential of QXG, particularly in the context of automated driving, where it can rationalize decisions by linking the graph with observed actions. These explanations can serve diverse purposes, from informing passengers and alerting vulnerable road users to enabling post-hoc analysis of prior behaviors.

Nassim Belmecheri, Arnaud Gotlieb, Nadjib Lazaar et al.

We present the Qualitative Explainable Graph (QXG): a unified symbolic and qualitative representation for scene understanding in urban mobility. QXG enables the interpretation of an automated vehicle's environment using sensor data and machine learning models. It leverages spatio-temporal graphs and qualitative constraints to extract scene semantics from raw sensor inputs, such as LiDAR and camera data, offering an intelligible scene model. Crucially, QXG can be incrementally constructed in real-time, making it a versatile tool for in-vehicle explanations and real-time decision-making across various sensor types. Our research showcases the transformative potential of QXG, particularly in the context of automated driving, where it elucidates decision rationales by linking the graph with vehicle actions. These explanations serve diverse purposes, from informing passengers and alerting vulnerable road users (VRUs) to enabling post-analysis of prior behaviours.

Dennis Gross, Helge Spieker, Arnaud Gotlieb et al.

High-level Computer-Aided Process Planning (CAPP) generates manufacturing process plans from part specifications. It suffers from limited dataset availability in industry, reducing model generalization. We propose a semi-supervised learning approach to improve transformer-based CAPP transformer models without manual labeling. An oracle, trained on available transformer behaviour data, filters correct predictions from unseen parts, which are then used for one-shot retraining. Experiments on small-scale datasets with simulated ground truth across the full data distribution show consistent accuracy gains over baselines, demonstrating the method's effectiveness in data-scarce manufacturing environments.

Clotilde Brayé, Aurélien Bricout, Arnaud Gotlieb et al.

Medical Intelligent Systems (MIS) are increasingly integrated into healthcare workflows, offering significant benefits but also raising critical safety and ethical concerns. According to the European Union AI Act, most MIS will be classified as high-risk systems, requiring a formal risk management process to ensure compliance with the ethical requirements of trustworthy AI. In this context, we focus on risk reduction optimization problems, which aim to reduce risks with ethical considerations by finding the best balanced assignment of risk assessment values according to their coverage of trustworthy AI ethical requirements. We formalize this problem as a constrained optimization task and investigate three resolution paradigms: Mixed Integer Programming (MIP), Satisfiability (SAT), and Constraint Programming(CP).Our contributions include the mathematical formulation of this optimization problem, its modeling with the Minizinc constraint modeling language, and a comparative experimental study that analyzes the performance, expressiveness, and scalability of each approach to solving. From the identified limits of the methodology, we draw some perspectives of this work regarding the integration of the Minizinc model into a complete trustworthy AI ethical risk management process for MIS.

Dennis Gross, Helge Spieker, Arnaud Gotlieb

In this paper, we introduce LLMCHECKER, a model-checking-based verification method to verify the probabilistic computation tree logic (PCTL) properties of an LLM text generation process. We empirically show that only a limited number of tokens are typically chosen during text generation, which are not always the same. This insight drives the creation of $α$-$k$-bounded text generation, narrowing the focus to the $α$ maximal cumulative probability on the top-$k$ tokens at every step of the text generation process. Our verification method considers an initial string and the subsequent top-$k$ tokens while accommodating diverse text quantification methods, such as evaluating text quality and biases. The threshold $α$ further reduces the selected tokens, only choosing those that exceed or meet it in cumulative probability. LLMCHECKER then allows us to formally verify the PCTL properties of $α$-$k$-bounded LLMs. We demonstrate the applicability of our method in several LLMs, including Llama, Gemma, Mistral, Genstruct, and BERT. To our knowledge, this is the first time PCTL-based model checking has been used to check the consistency of the LLM text generation process.

Helge Spieker, Jørn Eirik Betten, Arnaud Gotlieb et al.

Explainable AI (XAI) is essential for validating and trusting models in safety-critical applications like autonomous driving. However, the reliability of XAI is challenged by the Rashomon effect, where multiple, equally accurate models can offer divergent explanations for the same prediction. This paper provides the first empirical quantification of this effect for the task of action prediction in real-world driving scenes. Using Qualitative Explainable Graphs (QXGs) as a symbolic scene representation, we train Rashomon sets of two distinct model classes: interpretable, pair-based gradient boosting models and complex, graph-based Graph Neural Networks (GNNs). Using feature attribution methods, we measure the agreement of explanations both within and between these classes. Our results reveal significant explanation disagreement. Our findings suggest that explanation ambiguity is an inherent property of the problem, not just a modeling artifact.

Mohit Kumar Ahuja, Arnaud Gotlieb, Helge Spieker

Deep Learning (DL) has revolutionized the capabilities of vision-based systems (VBS) in critical applications such as autonomous driving, robotic surgery, critical infrastructure surveillance, air and maritime traffic control, etc. By analyzing images, voice, videos, or any type of complex signals, DL has considerably increased the situation awareness of these systems. At the same time, while relying more and more on trained DL models, the reliability and robustness of VBS have been challenged and it has become crucial to test thoroughly these models to assess their capabilities and potential errors. To discover faults in DL models, existing software testing methods have been adapted and refined accordingly. In this article, we provide an overview of these software testing methods, namely differential, metamorphic, mutation, and combinatorial testing, as well as adversarial perturbation testing and review some challenges in their deployment for boosting perception systems used in VBS. We also provide a first experimental comparative study on a classical benchmark used in VBS and discuss its results.

Mohamed-Bachir Belaid, Arnaud Gotlieb, Nadjib Lazaar

In most optimization problems, users have a clear understanding of the function to optimize (e.g., minimize the makespan for scheduling problems). However, the constraints may be difficult to state and their modelling often requires expertise in Constraint Programming. Active constraint acquisition has been successfully used to support non-experienced users in learning constraint networks through the generation of a sequence of queries. In this paper, we propose Learn&Optimize, a method to solve optimization problems with known objective function and unknown constraint network. It uses an active constraint acquisition algorithm which learns the unknown constraints and computes boundaries for the optimal solution during the learning process. As a result, our method allows users to solve optimization problems without learning the overall constraint network.

Helge Spieker, Arnaud Gotlieb

Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known boundaries and extracted features of COPs, it is possible to train the model to estimate boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP) which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver to find an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver to find near-optimal solutions early during search.

Mohit Kumar Ahuja, Mohamed-Bachir Belaid, Pierre Bernabé et al.

Trustworthiness is a central requirement for the acceptance and success of human-centered artificial intelligence (AI). To deem an AI system as trustworthy, it is crucial to assess its behaviour and characteristics against a gold standard of Trustworthy AI, consisting of guidelines, requirements, or only expectations. While AI systems are highly complex, their implementations are still based on software. The software engineering community has a long-established toolbox for the assessment of software systems, especially in the context of software testing. In this paper, we argue for the application of software engineering and testing practices for the assessment of trustworthy AI. We make the connection between the seven key requirements as defined by the European Commission's AI high-level expert group and established procedures from software engineering and raise questions for future work.

Helge Spieker, Arnaud Gotlieb

Constraint Optimization Problems (COP) are often considered without sufficient knowledge on the boundaries of the objective variable to optimize. When available, tight boundaries are helpful to prune the search space or estimate problem characteristics. Finding close boundaries, that correctly under- and overestimate the optimum, is almost impossible without actually solving the COP. This paper introduces Bion, a novel approach for boundary estimation by learning from previously solved instances of the COP. Based on supervised machine learning, Bion is problem-specific and solver-independent and can be applied to any COP which is repeatedly solved with different data inputs. An experimental evaluation over seven realistic COPs shows that an estimation model can be trained to prune the objective variables' domains by over 80%. By evaluating the estimated boundaries with various COP solvers, we find that Bion improves the solving process for some problems, although the effect of closer bounds is generally problem-dependent.

Helge Spieker, Arnaud Gotlieb

Metamorphic Testing is a software testing paradigm which aims at using necessary properties of a system-under-test, called metamorphic relations, to either check its expected outputs, or to generate new test cases. Metamorphic Testing has been successful to test programs for which a full oracle is not available or to test programs for which there are uncertainties on expected outputs such as learning systems. In this article, we propose Adaptive Metamorphic Testing as a generalization of a simple yet powerful reinforcement learning technique, namely contextual bandits, to select one of the multiple metamorphic relations available for a program. By using contextual bandits, Adaptive Metamorphic Testing learns which metamorphic relations are likely to transform a source test case, such that it has higher chance to discover faults. We present experimental results over two major case studies in machine learning, namely image classification and object detection, and identify weaknesses and robustness boundaries. Adaptive Metamorphic Testing efficiently identifies weaknesses of the tested systems in context of the source test case.

Morten Mossige, Arnaud Gotlieb, Helge Spieker et al.

Testing cyber-physical systems involves the execution of test cases on target-machines equipped with the latest release of a software control system. When testing industrial robots, it is common that the target machines need to share some common resources, e.g., costly hardware devices, and so there is a need to schedule test case execution on the target machines, accounting for these shared resources. With a large number of such tests executed on a regular basis, this scheduling becomes difficult to manage manually. In fact, with manual test execution planning and scheduling, some robots may remain unoccupied for long periods of time and some test cases may not be executed. This paper introduces TC-Sched, a time-aware method for automated test case execution scheduling. TC-Sched uses Constraint Programming to schedule tests to run on multiple machines constrained by the tests' access to shared resources, such as measurement or networking devices. The CP model is written in SICStus Prolog and uses the Cumulatives global constraint. Given a set of test cases, a set of machines, and a set of shared resources, TC-Sched produces an execution schedule where each test is executed once with minimal time between when a source code change is committed and the test results are reported to the developer. Experiments reveal that TC-Sched can schedule 500 test cases over 100 machines in less than 4 minutes for 99.5% of the instances. In addition, TC-Sched largely outperforms simpler methods based on a greedy algorithm and is suitable for deployment on industrial robot testing.

Helge Spieker, Arnaud Gotlieb

Testing the implementation of deep learning systems and their training routines is crucial to maintain a reliable code base. Modern software development employs processes, such as Continuous Integration, in which changes to the software are frequently integrated and tested. However, testing the training routines requires running them and fully training a deep learning model can be resource-intensive, when using the full data set. Using only a subset of the training data can improve test run time, but can also reduce its effectiveness. We evaluate different ways for training set reduction and their ability to mimic the characteristics of model training with the original full data set. Our results underline the usefulness of training set reduction, especially in resource-constrained environments.

Helge Spieker, Arnaud Gotlieb, Dusica Marijan et al.

Testing in Continuous Integration (CI) involves test case prioritization, selection, and execution at each cycle. Selecting the most promising test cases to detect bugs is hard if there are uncertainties on the impact of committed code changes or, if traceability links between code and tests are not available. This paper introduces Retecs, a new method for automatically learning test case selection and prioritization in CI with the goal to minimize the round-trip time between code commits and developer feedback on failed test cases. The Retecs method uses reinforcement learning to select and prioritize test cases according to their duration, previous last execution and failure history. In a constantly changing environment, where new test cases are created and obsolete test cases are deleted, the Retecs method learns to prioritize error-prone test cases higher under guidance of a reward function and by observing previous CI cycles. By applying Retecs on data extracted from three industrial case studies, we show for the first time that reinforcement learning enables fruitful automatic adaptive test case selection and prioritization in CI and regression testing.

Helge Spieker, Arnaud Gotlieb, Morten Mossige

Multi-cycle assignment problems address scenarios where a series of general assignment problems has to be solved sequentially. Subsequent cycles can differ from previous ones due to changing availability or creation of tasks and agents, which makes an upfront static schedule infeasible and introduces uncertainty in the task-agent assignment process. We consider the setting where, besides profit maximization, it is also desired to maintain diverse assignments for tasks and agents, such that all tasks have been assigned to all agents over subsequent cycles. This problem of multi-cycle assignment with rotational diversity is approached in two sub-problems: The outer problem which augments the original profit maximization objective with additional information about the state of rotational diversity while the inner problem solves the adjusted general assignment problem in a single execution of the model. We discuss strategies to augment the profit values and evaluate them experimentally. The method's efficacy is shown in three case studies: multi-cycle variants of the multiple knapsack and the multiple subset sum problems, and a real-world case study on the test case selection and assignment problem from the software engineering domain.

Guillaume Bécan, Razieh Behjati, Arnaud Gotlieb et al.

Feature modeling is a widely used formalism to characterize a set of products (also called configurations). As a manual elaboration is a long and arduous task, numerous techniques have been proposed to reverse engineer feature models from various kinds of artefacts. But none of them synthesize feature attributes (or constraints over attributes) despite the practical relevance of attributes for documenting the different values across a range of products. In this report, we develop an algorithm for synthesizing attributed feature models given a set of product descriptions. We present sound, complete, and parametrizable techniques for computing all possible hierarchies, feature groups, placements of feature attributes, domain values, and constraints. We perform a complexity analysis w.r.t. number of features, attributes, configurations, and domain size. We also evaluate the scalability of our synthesis procedure using randomized configuration matrices. This report is a first step that aims to describe the foundations for synthesizing attributed feature models.

Sébastien Bardin, Arnaud Gotlieb

Arrays are ubiquitous in the context of software verification. However, effective reasoning over arrays is still rare in CP, as local reasoning is dramatically ill-conditioned for constraints over arrays. In this paper, we propose an approach combining both global symbolic reasoning and local consistency filtering in order to solve constraint systems involving arrays (with accesses, updates and size constraints) and finite-domain constraints over their elements and indexes. Our approach, named FDCC, is based on a combination of a congruence closure algorithm for the standard theory of arrays and a CP solver over finite domains. The tricky part of the work lies in the bi-directional communication mechanism between both solvers. We identify the significant information to share, and design ways to master the communication overhead. Experiments on random instances show that FDCC solves more formulas than any portfolio combination of the two solvers taken in isolation, while overhead is kept reasonable.

Roberto Bagnara, Matthieu Carlier, Roberta Gori et al.

Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms. For this reason, verification and validation of floating-point computations is a hot research topic. An important verification technique, especially in some industrial sectors, is testing. However, generating test data for floating-point intensive programs proved to be a challenging problem. Existing approaches usually resort to random or search-based test data generation, but without symbolic reasoning it is almost impossible to generate test inputs that execute complex paths controlled by floating-point computations. Moreover, as constraint solvers over the reals or the rationals do not natively support the handling of rounding errors, the need arises for efficient constraint solvers over floating-point domains. In this paper, we present and fully justify improved algorithms for the propagation of arithmetic IEEE 754 binary floating-point constraints. The key point of these algorithms is a generalization of an idea by B. Marre and C. Michel that exploits a property of the representation of floating-point numbers.