# Stochastic Fairness and Language-Theoretic Fairness in Planning on Nondeterministic Domains

arXiv: https://arxiv.org/abs/1912.11203 · HTML: https://mlsanity.com/paper/1912.11203/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2019.

## Built on by (most cited first, 5 of 5)

- [Flexible FOND Planning with Explicit Fairness Assumptions](https://mlsanity.com/paper/2103.08391/) (2021)
- [Planning for Temporally Extended Goals in Pure-Past Linear Temporal Logic: A Polynomial Reduction to Standard Planning](https://mlsanity.com/paper/2204.09960/) (2022)
- [Abstraction of Nondeterministic Situation Calculus Action Theories -- Extended Version](https://mlsanity.com/paper/2305.14222/) (2023)
- [Temporally Extended Goal Recognition in Fully Observable Non-Deterministic Domain Models](https://mlsanity.com/paper/2306.08680/) (2023)
- [Recognizing LTLf/PLTLf Goals in Fully Observable Non-Deterministic Domain Models](https://mlsanity.com/paper/2103.11692/) (2021)

## Abstract (arXiv)

We address two central notions of fairness in the literature of planning on nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically using possibly unknown probabilities. The second, which is language-theoretic, assumes that if an action is taken from a given state infinitely often then all its possible outcomes should appear infinitely often (we call this state-action fairness). While the two notions coincide for standard reachability goals, they diverge for temporally extended goals. This important difference has been overlooked in the planning literature, and we argue has led to confusion in a number of published algorithms which use reductions that were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide an optimal sound and complete algorithm for solving state-action fair planning for LTL/LTLf goals, as well as a correct proof of the lower bound of the goal-complexity (our proof is general enough that it provides new proofs also for the no-fairness and stochastic-fairness cases). Overall, we show that stochastic fairness is better behaved than state-action fairness.