# Deciding Hyperproperties

arXiv: https://arxiv.org/abs/1606.07047 · HTML: https://mlsanity.com/paper/1606.07047/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2016.

## Built on by (most cited first, 3 of 3)

- [Temporal Ensemble Logic](https://mlsanity.com/paper/2408.14443/) (2024)
- [HypRL: Reinforcement Learning of Control Policies for Hyperproperties](https://mlsanity.com/paper/2504.04675/) (2025)
- [Bayesian Statistical Model Checking for Multi-agent Systems using HyperPCTL*](https://mlsanity.com/paper/2209.02672/) (2022)

## Abstract (arXiv)

Hyperproperties, like observational determinism or symmetry, cannot be expressed as properties of individual computation traces, because they describe a relation between multiple computation traces. HyperLTL is a temporal logic that captures such relations through trace variables, which are introduced through existential and universal trace quantifiers and can be used to refer to multiple computations at the same time. In this paper, we study the satisfiability problem of HyperLTL. We show that the problem is PSPACE-complete for alternation-free formulas (and, hence, no more expensive than LTL satisfiability), EXPSPACE-complete for exists-forall-formulas, and undecidable for forall-exists-formulas. Many practical hyperproperties can be expressed as alternation-free formulas. Our results show that both satisfiability and implication are decidable for such properties.