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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…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step…
This report details the translation and testing of multiple benchmarks, including the Six Vehicle Platoon, Two Bouncing Ball, Three Tank System, and Four-Dimensional Linear Switching, which represent continuous and hybrid systems. These…
Simulink is widely used in industrial design processes to model increasingly complex embedded control systems. Thus, their formal analysis is highly desirable. However, this comes with two major challenges: First, Simulink models often…
Hierarchical block diagrams (HBDs) are at the heart of embedded system design tools, including Simulink. Numerous translations exist from HBDs into languages with formal semantics, amenable to formal verification. However, none of these…
Reachability analysis for hybrid systems is an active area of development and has resulted in many promising prototype tools. Most of these tools allow users to express hybrid system as automata with a set of ordinary differential equations…
Simulink is the de facto industrial standard for designing embedded control systems. When dealing with the formal verification of Simulink models, we face the problem of translating the graphical language of Simulink, namely, hierarchical…
In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in…
A key module in neural transformer-based deep architectures is positional encoding. This module enables a suitable way to encode positional information as input for transformer neural layers. This success has been rooted in the use of…
In current practice a formal analysis of hybrid system models is assertion-based. The work presented here is based on features that look beyond functional correctness toward a quantitative evaluation of behavioral attributes. A feature…
We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solid-state spin qubits, or superconducting devices. We summarize and compare different coupling…
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete…
Linear operations on coefficients in the spherical harmonics (SH) transform domain that again yield SH-domain coefficients are an important toolset in many disciplines of research and engineering. They comprise rotations, spatially…
We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a faithful representation of arbitrary syntactic objects in…
We extend abstract interpretation for the purpose of verifying hybrid systems. Abstraction has been playing an important role in many verification methodologies for hybrid systems, but some special care is needed for abstraction of…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…