# Solution independence and self-referential instances

arXiv: https://arxiv.org/abs/2605.02174 · HTML: https://mlsanity.com/paper/2605.02174/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2026.

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

- [Can Machines Really See Objects in Images? A Study Based on Syntactic Distance and Visual Self-Referential Instances](https://mlsanity.com/paper/2606.29416/) (2026)

## Abstract (arXiv)

In this paper, we investigate the hitting set problem and demonstrate that solution independence is the crucial property underlying the construction of self-referential instances. As a special case of the hitting set problem, the vertex cover problem lacks the solution independence property. This distinction accounts for its ability to evade exhaustive search, as correlations among candidate solutions can be leveraged to compress the overall search space. In contrast, the dominating set problem on hypergraphs, which is also a special case of the hitting set problem, satisfies the solution independence property, thereby enabling the construction of self-referential instances. Moreover, we prove that these self-referential instances possess an irreducible property, implying that any algorithm for solving such instances must process nearly the entire graph to yield a correct solution.