# Revealing POMDPs: Qualitative and Quantitative Analysis for Parity Objectives

arXiv: https://arxiv.org/abs/2511.13134 · HTML: https://mlsanity.com/paper/2511.13134/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2025.

## Built on by (most cited first, 2 of 2)

- [REBA: A Revealed Belief Automaton Framework for Online Planning in Continuous POMDPs](https://mlsanity.com/paper/2606.21971/) (2026)
- [On the Complexity Gap Between POMDPs and Multi-Environment POMDPs](https://mlsanity.com/paper/2610.15010/) (2026)

## Abstract (arXiv)

Partially observable Markov decision processes (POMDPs) are a central model for uncertainty in sequential decision making. The most basic objective is the reachability objective, where a target set must be eventually visited, and the more general parity objectives can model all omega-regular specifications. For such objectives, the computational analysis problems are the following: (a) qualitative analysis that asks whether the objective can be satisfied with probability 1 (almost-sure winning) or probability arbitrarily close to 1 (limit-sure winning); and (b) quantitative analysis that asks for the approximation of the optimal probability of satisfying the objective. For general POMDPs, almost-sure analysis for reachability objectives is EXPTIME-complete, but limit-sure and quantitative analyses for reachability objectives are undecidable; almost-sure, limit-sure, and quantitative analyses for parity objectives are all undecidable. A special class of POMDPs, called revealing POMDPs, has been studied recently in several works, and for this subclass the almost-sure analysis for parity objectives was shown to be EXPTIME-complete. In this work, we show that for revealing POMDPs the limit-sure analysis for parity objectives is EXPTIME-complete, and even the quantitative analysis for parity objectives can be achieved in EXPTIME.