Canonical Representations of k-Safety Hyperproperties

TL;DR

This paper introduces a canonical automata-theoret representation for regular k-safety hyperproperties, enabling improved analysis, comparison, and learning of these properties, which are crucial for information-flow policies.

Contribution

It provides the first finite automaton representation for regular k-safety hyperproperties, facilitating automata-based algorithms and learning methods for these complex properties.

Findings

Finite automaton representation for regular k-safety hyperproperties

Complexity bounds for automata construction from HyperLTL formulas

A learning algorithm for hyperproperties based on L* automata learning

Abstract

Hyperproperties elevate the traditional view of trace properties form sets of traces to sets of sets of traces and provide a formalism for expressing information-flow policies. For trace properties, algorithms for verification, monitoring, and synthesis are typically based on a representation of the properties as omega-automata. For hyperproperties, a similar, canonical automata-theoretic representation is, so far, missing. This is a serious obstacle for the development of algorithms, because basic constructions, such as learning algorithms, cannot be applied. In this paper, we present a canonical representation for the widely used class of regular k-safety hyperproperties, which includes important polices such as noninterference. We show that a regular k-safety hyperproperty S can be represented by a finite automaton, where each word accepted by the automaton represents a violation of S. The representation provides an automata-theoretic approach to regular k-safety hyperproperties and allows us to compare regular k-safety hyperproperties, simplify them, and learn such hyperproperties. We investigate the problem of constructing automata for regular k-safety hyperproperties in general and from formulas in HyperLTL, and provide complexity bounds for the different translations. We also present a learning algorithm for regular k-safety hyperproperties based on the L* learning algorithm for deterministic finite automata.