Sapo: Reachability Computation and Parameter Synthesis of Polynomial Dynamical Systems

Sapo is a C++ tool for the formal analysis of polynomial dynamical systems. Its main features are: 1) Reachability computation, i.e., the calculation of the set of states reachable from a set of initial conditions, and 2) Parameter synthesis, i.e., the refinement of a set of parameters so that the system satisfies a given specification. Sapo can represent reachable sets as unions of boxes, parallelotopes, or parallelotope bundles (symbolic representation of polytopes). Sets of parameters are represented with polytopes while specifications are formalized as Signal Temporal Logic (STL) formulas

Approximated Symbolic Computations over Hybrid Automata

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms.Comment: In Proceedings HAS 2013, arXiv:1308.490

A Formalization of Robustness for Deep Neural Networks

Deep neural networks have been shown to lack robustness to small input perturbations. The process of generating the perturbations that expose the lack of robustness of neural networks is known as adversarial input generation. This process depends on the goals and capabilities of the adversary, In this paper, we propose a unifying formalization of the adversarial input generation process from a formal methods perspective. We provide a definition of robustness that is general enough to capture different formulations. The expressiveness of our formalization is shown by modeling and comparing a variety of adversarial attack techniques

Reachability computation for polynomial dynamical systems

This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system. The problem is well-known for being difficult when nonlinear systems are considered. In this regard, we propose three reachability methods that differ in the set representation. The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets. The latter is a new data structure for the symbolic representation of polytopes. Our methods exploit the Bernstein expansion of polynomials to bound the images of sets. The scalability and precision of the presented methods are analyzed on a number of dynamical systems, in comparison with other existing approaches

Approximated Symbolic Computations over Hybrid Automata

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms

Counterexample-Guided Data Augmentation

We present a novel framework for augmenting data sets for machine learning based on counterexamples. Counterexamples are misclassified examples that have important properties for retraining and improving the model. Key components of our framework include a counterexample generator, which produces data items that are misclassified by the model and error tables, a novel data structure that stores information pertaining to misclassifications. Error tables can be used to explain the model's vulnerabilities and are used to efficiently generate counterexamples for augmentation. We show the efficacy of the proposed framework by comparing it to classical augmentation techniques on a case study of object detection in autonomous driving based on deep neural networks

3D Environment Modeling for Falsification and Beyond with Scenic 3.0

We present a major new version of Scenic, a probabilistic programming language for writing formal models of the environments of cyber-physical systems. Scenic has been successfully used for the design and analysis of CPS in a variety of domains, but earlier versions are limited to environments which are essentially two-dimensional. In this paper, we extend Scenic with native support for 3D geometry, introducing new syntax which provides expressive ways to describe 3D configurations while preserving the simplicity and readability of the language. We replace Scenic's simplistic representation of objects as boxes with precise modeling of complex shapes, including a ray tracing-based visibility system that accounts for object occlusion. We also extend the language to support arbitrary temporal requirements expressed in LTL, and build an extensible Scenic parser generated from a formal grammar of the language. Finally, we illustrate the new application domains these features enable with case studies that would have been impossible to accurately model in Scenic 2.Comment: 13 pages, 6 figures. Full version of a CAV 2023 tool paper, to appear in the Springer Lecture Notes in Computer Science serie