# Predicate abstraction for hyperliveness verification

## TL;DR

This paper introduces a new automated method to verify complex system properties in infinite-state systems using predicate abstraction.

## Contribution

The novel method verifies ∀k∃l-safety properties in infinite-state systems using predicate abstraction and trace quantification strategies.

## Key findings

- The method combines universal and existential trace quantification to capture hyperliveness properties.
- It enables verification of properties like generalized non-interference and program refinement.
- The approach uses predicate abstraction and program reduction for efficient analysis.

## Abstract

Temporal hyperproperties are system properties that relate multiple execution traces. In finite-state systems, temporal hyperproperties are supported by model-checking algorithms, and tools for general temporal logics like HyperLTL exist. In infinite-state systems, the analysis of temporal hyperproperties has, so far, been limited to k-safety properties, i.e., properties that stipulate the absence of a bad interaction between any k traces. In this paper, we present an automated method for the verification of \documentclass[12pt]{minimal}
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\begin{document}$$\forall ^k\exists ^l$$\end{document}∀k∃l-safety properties in infinite-state systems. A \documentclass[12pt]{minimal}
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\begin{document}$$\forall ^k\exists ^l$$\end{document}∀k∃l-safety property stipulates that for any k traces, there exist l traces such that the resulting \documentclass[12pt]{minimal}
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\begin{document}$$k+l$$\end{document}k+l traces do not interact badly. This combination of universal and existential quantification captures many properties beyond k-safety, including hyperliveness properties such as generalized non-interference or program refinement. Our verification method is based on a strategy-based instantiation of existential trace quantification combined with a program reduction, both in the context of a fixed predicate abstraction.