# Algorithms for Deciding the Safety of States in Fully Observable Non-deterministic Problems: Technical Report

arXiv: https://arxiv.org/abs/2603.15282 · HTML: https://mlsanity.com/paper/2603.15282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 2 of 2)

- [ASNets: Deep Learning for Generalised Planning](https://mlsanity.com/paper/1908.01362/) (2019)
- [Topological Value Iteration Algorithms](https://mlsanity.com/paper/1401.3910/) (2014)

## Abstract (arXiv)

Learned action policies are increasingly popular in sequential decision-making, but suffer from a lack of safety guarantees. Recent work introduced a pipeline for testing the safety of such policies under initial-state and action-outcome non-determinism. At the pipeline's core, is the problem of deciding whether a state is safe (a safe policy exists from the state) and finding faults, which are state-action pairs that transition from a safe state to an unsafe one. Their most effective algorithm for deciding safety, TarjanSafe, is effective on their benchmarks, but we show that it has exponential worst-case runtime with respect to the state space. A linear-time alternative exists, but it is slower in practice. We close this gap with a new policy-iteration algorithm iPI, that combines the best of both: it matches TarjanSafe's best-case runtime while guaranteeing a polynomial worst-case. Experiments confirm our theory and show that in problems amenable to TarjanSafe iPI has similar performance, whereas in ill-suited problems iPI scales exponentially better.