# Finding hardness reductions automatically using SAT solvers

arXiv: https://arxiv.org/abs/2402.06397 · HTML: https://mlsanity.com/paper/2402.06397/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [Inserting one edge into a simple drawing is hard](https://mlsanity.com/paper/1909.07347/) (2019)
- [Tatamibari is NP-complete](https://mlsanity.com/paper/2003.08331/) (2020)
- [Topological Drawings meet Classical Theorems from Convex Geometry](https://mlsanity.com/paper/2005.12568/) (2020)

## Abstract (arXiv)

In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in literature are found by hand, we present an algorithm to construct gadgets in a fully automated way. Using our framework which is based on SAT, we present the first thorough study of the completion problem on sign mappings with forbidden substructures by classifying thousands of structures for which the completion problem is NP-complete. Our list in particular includes interior triple systems, which were introduced by Knuth towards an axiomatization of planar point configurations. Last but not least, we give an infinite family of structures generalizing interior triple system to higher dimensions for which the completion problem is NP-complete.