Unifying Hyper and Epistemic Temporal Logic

TL;DR

This paper compares two advanced temporal logics for security requirements, establishes their incomparability, and introduces a unifying linear past extension with decidable model-checking, advancing understanding of their expressiveness and computational complexity.

Contribution

It introduces a unifying linear past extension of HyperCTL* that can express KCTL* properties, and proves the decidability and complexity of model-checking this logic.

Findings

KCTL* and HyperCTL* are expressively incomparable.

The proposed linear past extension can translate KCTL* in linear time.

Model-checking for the new logic is decidable with known complexity.

Abstract

In the literature, two powerful temporal logic formalisms have been proposed for expressing information flow security requirements, that in general, go beyond regular properties. One is classic, based on the knowledge modalities of epistemic logic. The other one, the so called hyper logic, is more recent and subsumes many proposals from the literature; it is based on explicit and simultaneous quantification over multiple paths. In an attempt to better understand how these logics compare with each other, we consider the logic KCTL* (the extension of CTL* with knowledge modalities and synchronous perfect recall semantics) and HyperCTL*. We first establish that KCTL* and HyperCTL* are expressively incomparable. Second, we introduce and study a natural linear past extension of HyperCTL* to unify KCTL* and HyperCTL*; indeed, we show that KCTL* can be easily translated in linear time into the proposed logic. Moreover, we show that the model-checking problem for this novel logic is decidable, and we provide its exact computational complexity in terms of a new measure of path quantifiers' alternation. For this, we settle open complexity issues for unrestricted quantified propositional temporal logic.