Related papers: Reflections on Termination of Linear Loops
We consider linear single-path loops of the form \[ \textbf{while} \quad \varphi \quad \textbf{do} \quad \vec{x} \gets A \vec{x} + \vec{b} \quad \textbf{end} \] where $\vec{x}$ is a vector of variables, the loop guard $\varphi$ is a…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
Feedback optimization algorithms compute inputs to a system using real-time output measurements, which helps mitigate the effects of disturbances. However, existing work often models both system dynamics and computations in either discrete…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
The link between structure and behavior is central to System Dynamics, but effective tools for understanding that relationship still elude us. The current state of the art in the field of loop dominance analysis relies on either…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Combined modeling and verification of dynamic systems and the data they operate on has gained momentum in AI and in several application domains. We investigate the expressive yet concise framework of data-aware dynamic systems (DDS),…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…
A syntactic model is presented for the specification of finite-state synchronous digital logic systems with complex input/output interfaces, which control the flow of data between opaque computational elements, and for the composition of…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…