Related papers: Dynamic Logics of Dynamical Systems
The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
This paper presents a dynamic logic $d\mathcal{L}_\text{CHP}$ for compositional deductive verification of communicating hybrid programs (CHPs). CHPs go beyond the traditional mixed discrete and continuous dynamics of hybrid systems by…
We present Logical Robots, an interactive multi-agent simulation platform where autonomous robot behavior is specified declaratively in the logic programming language Logica. Robot behavior is defined by logical predicates that map…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
We propose $\mathcal{E}^{\downarrow}$-logic as a formal foundation for the specification and development of event-based systems with local data states. The logic is intended to cover a broad range of abstraction levels from abstract…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
In this paper, we consider the notion of resilience of a dynamical system, defined by the maximum disturbance a controlled dynamical system can withstand while satisfying given temporal logic specifications. Given a dynamical system and a…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
This work presents three increasingly expressive Dynamic Logics in which the programs are CCS processes (sCCS-PDL, CCS-PDL and XCCS-PDL). Their goal is to reason about properties of concurrent programs and systems described using CCS. In…
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…