# Synthesizing Reactive Systems from Hyperproperties

## TL;DR

This paper explores the synthesis of reactive systems from hyperproperties expressed in HyperLTL, identifying decidable fragments and providing semi-decision procedures with promising experimental results.

## Contribution

It characterizes decidability boundaries for HyperLTL synthesis and introduces a semi-decision method for universal HyperLTL with practical implementation.

## Key findings

- Decidability for certain HyperLTL fragments.
- Semi-decision procedure for universal HyperLTL.
- Prototype implementation shows promising results.

## Abstract

We study the reactive synthesis problem for hyperproperties given as formulas of the temporal logic HyperLTL. Hyperproperties generalize trace properties, i.e., sets of traces, to sets of sets of traces. Typical examples are information-flow policies like noninterference, which stipulate that no sensitive data must leak into the public domain. Such properties cannot be expressed in standard linear or branching-time temporal logics like LTL, CTL, or CTL$^*$. We show that, while the synthesis problem is undecidable for full HyperLTL, it remains decidable for the $\exists^*$, $\exists^*\forall^1$, and the $\mathit{linear}\;\forall^*$ fragments. Beyond these fragments, the synthesis problem immediately becomes undecidable. For universal HyperLTL, we present a semi-decision procedure that constructs implementations and counterexamples up to a given bound. We report encouraging experimental results obtained with a prototype implementation on example specifications with hyperproperties like symmetric responses, secrecy, and information-flow.