# Control Synthesis for Permutation-Symmetric High-Dimensional Systems With Counting Constraints

arXiv: https://arxiv.org/abs/1706.07863 · HTML: https://mlsanity.com/paper/1706.07863/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2017.

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

- [Homomorphic Mappings for Value-Preserving State Aggregation in Markov Decision Processes](https://mlsanity.com/paper/2510.09965/) (2025)

## Abstract (arXiv)

General purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this work we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably correct controllers for systems with tens of thousands of states. The key ingredients of the solution are an aggregate abstraction procedure for mildly heterogeneous systems and a formulation of counting constraints as linear inequalities.