Related papers: A composition theorem for bisimulation functions
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…
In this paper, we provide a compositional framework for synthesizing hybrid controllers for interconnected discrete-time control systems enforcing specifications expressed by co-Buchi automata. In particular, we first decompose the given…
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types,…
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…
We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The…
Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of…
In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space…
The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the…
Correlation functions, such as static and dynamic structure factors, offer a versatile approach to analyzing atomic-scale structure and dynamics. By having access to the full dynamics from atomistic simulations, they serve as valuable tools…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
Hybrid systems are a compact and natural mechanism with which to address problems in robotics. This work introduces an approach to learning hybrid systems from demonstrations, with an emphasis on extracting models that are explicitly…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…