# On Local Domain Symmetry for Model Expansion

arXiv: https://arxiv.org/abs/1608.02688 · HTML: https://mlsanity.com/paper/1608.02688/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2016.

## Built on by (most cited first, 7 of 7)

- [Lifting Symmetry Breaking Constraints with Inductive Logic Programming](https://mlsanity.com/paper/2112.11806/) (2021)
- [Efficient lifting of symmetry breaking constraints for complex combinatorial problems](https://mlsanity.com/paper/2205.07129/) (2022)
- [A Model-Oriented Approach for Lifting Symmetries in Answer Set Programming](https://mlsanity.com/paper/2208.03095/) (2022)
- [Using Symmetries to Lift Satisfiability Checking](https://mlsanity.com/paper/2311.03424/) (2023)
- [Symmetry breaking for inductive logic programming](https://mlsanity.com/paper/2508.06263/) (2025)
- [Towards Mass Spectrum Analysis with ASP](https://mlsanity.com/paper/2512.16780/) (2025)
- [Streamliners for Answer Set Programming](https://mlsanity.com/paper/2604.19251/) (2026)

## Abstract (arXiv)

Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification of local domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared to SBASS , a symmetry breaking technique for answer set programming.