# Sparsity-Sensitive Finite Abstraction

## TL;DR

This paper introduces a sparsity-sensitive abstraction algorithm that significantly accelerates the process of creating finite models for high-dimensional systems with sparse interconnections, enabling applications previously infeasible due to computational constraints.

## Contribution

The authors propose a simple modification to existing abstraction algorithms that exploits system sparsity, achieving substantial speed-ups while maintaining accuracy.

## Key findings

- Speed-up in abstraction computation for high-dimensional systems
- Successful synthesis of a safety controller for a 12D system
- Efficient abstraction of a 51D vehicular traffic network

## Abstract

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network.