Finite Uniform Bisimulations for Linear Systems with Finite Input Alphabets

TL;DR

This paper introduces finite uniform bisimulations for linear discrete-time systems with finite input sets, providing conditions for their existence and algorithms for their computation, supported by illustrative examples.

Contribution

It formulates a new notion of regular finite uniform bisimulation and derives conditions and algorithms for their computation in linear systems.

Findings

Sufficient conditions for the existence of finite uniform bisimulations.

Algorithms to compute finite uniform bisimulations.

Illustrative examples demonstrating the concepts.

Abstract

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite uniform bisimulation. We derive sufficient conditions for the existence of finite uniform bisimulations, and propose and analyze algorithms to compute finite uniform bisimulations when the sufficient conditions are satisfied. We investigate the necessary conditions, and conclude with a set of illustrative examples.