# Parameterized Verification of Algorithms for Oblivious Robots on a Ring

## TL;DR

This paper investigates the verification of algorithms for anonymous robots on a ring, demonstrating decidability results for safety properties in certain cases and employing SMT-solvers for automated verification.

## Contribution

It is the first to analyze parameterized verification of such algorithms, providing decidability results and encoding techniques using Presburger arithmetic and SMT-solvers.

## Key findings

- Safety verification is undecidable in asynchronous settings.
- Safety properties are decidable in synchronous and certain asynchronous cases.
- Encoding protocols in Presburger arithmetic enables automated verification.

## Abstract

We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameter-ized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies.