Estimating worst-case execution time (WCET) is an important activity at early design stages of real-time systems. Based on WCET estimates, engineers make design and implementation decisions to ensure that task executions always complete before their specified deadlines. However, in practice, engineers often cannot provide precise point WCET estimates and prefer to provide plausible WCET ranges. Given a set of real-time tasks with such ranges, we provide an automated technique to determine for what WCET values the system is likely to meet its deadlines and, hence, operate safely with a probabilistic guarantee. Our approach combines a search algorithm for generating worst-case scheduling scenarios with polynomial logistic regression for inferring probabilistic safe WCET ranges. We evaluated our approach by applying it to three industrial systems from different domains and several synthetic systems. Our approach efficiently and accurately estimates probabilistic safe WCET ranges within which deadlines are likely to be satisfied with a high degree of confidence.

Software verification may yield spurious failures when environment assumptions are not accounted for. Environment assumptions are the expectations that a system or a component makes about its operational environment and are often specified in terms of conditions over the inputs of that system or component. In this article, we propose an approach to automatically infer environment assumptions for Cyber-Physical Systems (CPS). Our approach improves the state-of-the-art in three different ways: First, we learn assumptions for complex CPS models involving signal and numeric variables; second, the learned assumptions include arithmetic expressions defined over multiple variables; third, we identify the trade-off between soundness and coverage of environment assumptions and demonstrate the flexibility of our approach in prioritizing either of these criteria. We evaluate our approach using a public domain benchmark of CPS models from Lockheed Martin and a component of a satellite control system from LuxSpace, a satellite system provider. The results show that our approach outperforms state-of-the-art techniques on learning assumptions for CPS models, and further, when applied to our industrial CPS model, our approach is able to learn assumptions that are sufficiently close to the assumptions manually developed by engineers to be of practical value.

Black-box testing has been extensively applied to test models of Cyber-Physical systems (CPS) since these models are not often amenable to static and symbolic testing and verification. Black-box testing, however, requires to execute the model under test for a large number of candidate test inputs. This poses a challenge for a large and practically-important category of CPS models, known as compute-intensive CPS (CI-CPS) models, where a single simulation may take hours to complete. We propose a novel approach, namely ARIsTEO, to enable effective and efficient testing of CI-CPS models. Our approach embeds black-box testing into an iterative approximation-refinement loop. At the start, some sampled inputs and outputs of the CI-CPS model under test are used to generate a surrogate model that is faster to execute and can be subjected to black-box testing. Any failure-revealing test identified for the surrogate model is checked on the original model. If spurious, the test results are used to refine the surrogate model to be tested again. Otherwise, the test reveals a valid failure. We evaluated ARIsTEO by comparing it with S-Taliro, an open-source and industry-strength tool for testing CPS models. Our results, obtained based on five publicly-available CPS models, show that, on average, ARIsTEO is able to find 24% more requirements violations than S-Taliro and is 31% faster than S-Taliro in finding those violations. We further assessed the effectiveness and efficiency of ARIsTEO on a large industrial case study from the satellite domain. In contrast to S-Taliro, ARIsTEO successfully tested two different versions of this model and could identify three requirements violations, requiring four hours, on average, for each violation.

Signal-based temporal properties (SBTPs) characterize the behavior of a system when its inputs and outputs are signals over time; they are very common for the requirements specification of cyber-physical systems. Although there exist several specification languages for expressing SBTPs, such languages either do not easily allow the specification of important types of properties (such as spike or oscillatory behaviors), or are not supported by (efficient) trace-checking procedures.

Applying traditional testing techniques to Cyber-Physical Systems (CPS) is challenging due to the deep intertwining of software and hardware, and the complex, continuous interactions between the system and its environment. To alleviate these challenges we propose to conduct testing at early stages and over executable models of the system and its environment. Model testing of CPSs is however not without difficulties. The complexity and heterogeneity of CPSs renders necessary the combination of different modeling formalisms to build faithful models of their different components. The execution of CPS models thus requires an execution framework supporting the cosimulation of different types of models, including models of the software (e.g., SysML), hardware (e.g., SysML or Simulink), and physical environment (e.g., Simulink). Furthermore, to enable testing in realistic conditions, the cosimulation process must be (1) fast, so that thousands of simulations can be conducted in practical time, (2) controllable, to precisely emulate the expected runtime behavior of the system and, (3) observable, by producing simulation data enabling the detection of failures. To tackle these challenges, we propose a SysML-based modeling methodology for model testing of CPSs, and an efficient SysML-Simulink cosimulation framework. Our approach was validated on a case study from the satellite domain.