Related papers: Abstraction of Elementary Hybrid Systems by Variab…
Learning robust and generalisable abstractions from high-dimensional input data is a central challenge in machine learning and its applications to high-energy physics (HEP). Solutions of lower functional complexity are known to produce…
We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes…
Stochastic hybrid systems have received significant attentions as a relevant modelling framework describing many systems, from engineering to the life sciences: they enable the study of numerous applications, including transportation…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
Scientific software is, by its very nature, complex. It is mathematical and highly optimized which makes it prone to subtle bugs not as easily detected by traditional testing. We outline how symbolic execution can be used to write tests…
Memory safety is an essential correctness property of software systems. For programs operating on linked heap-allocated data structures, the problem of proving memory safety boils down to analyzing the possible shapes of data structures,…
We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the…
Elementary Object Systems (EOS) are a form of Petri Net (PN) where tokens carry internal PN. This model has been recently proposed for analysis of robustness of Multi Agent Systems. While EOS reachability is known to be undecidable, the…
Safety is critical in robotic tasks. Energy function based methods have been introduced to address the problem. To ensure safety in the presence of control limits, we need to design an energy function that results in persistently feasible…
Symbolic execution is a powerful program analysis technique that allows for the systematic exploration of all program paths. Path explosion, where the number of states to track becomes unwieldy, is one of the biggest challenges hindering…
We formalize the semantics of hybrid systems as sets of hybrid trajectories, including those generated by an hybrid transition system. We study the abstraction of hybrid trajectory semantics for verification, static analysis, and…
We introduce Exhaustive Symbolic Integration (ESI), a method that enumerates all symbolic functions up to a given complexity $k$ within a specified operator basis and determines which admit closed-form antiderivatives within the same class.…
In this extended abstract, we discuss the opportunity to formally verify that inference systems for probabilistic programming guarantee good performance. In particular, we focus on hybrid inference systems that combine exact and approximate…
The increasing prevalence of high-dimensional data demands efficient and scalable compression methods to support modern applications. However, existing techniques like PCA and Autoencoders often rely on auxiliary metadata or intricate…
Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to…
This paper studies the reduction (abstraction) of finite-state transition systems for control synthesis problems. We revisit the notion of alternating simulation equivalence (ASE), a more relaxed condition than alternating bisimulations, to…
Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a…
We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer…