# Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints

arXiv: https://arxiv.org/abs/2509.10716 · HTML: https://mlsanity.com/paper/2509.10716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2025.

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

- [VLPSA: Vision-Language-Poisson-Safe Actions for Full-Body Safety of Learned Policies](https://mlsanity.com/paper/2609.22462/) (2026)

## Abstract (arXiv)

This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system.