# Multi-Agent Safety Verification using Symmetry Transformations

arXiv: https://arxiv.org/abs/1911.00608 · HTML: https://mlsanity.com/paper/1911.00608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Exploiting Symmetry in Dynamics for Model-Based Reinforcement Learning with Asymmetric Rewards](https://mlsanity.com/paper/2403.19024/) (2024)

## Abstract (arXiv)

We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map solutions and to other solutions. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of virtual system which define symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of virtual system, we present a prototype tool CacheReach that builds a cache of reachtubes for this system, in a way that is agnostic of the representation of the reachsets and the reachability analysis subroutine used. Our experimental evaluation of CacheReach shows up to 66% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.