# Temporal Logics for Hyperproperties

@inproceedings{Clarkson2014TemporalLF, title={Temporal Logics for Hyperproperties}, author={Michael R. Clarkson and Bernd Finkbeiner and Masoud Koleini and Kristopher K. Micinski and Markus N. Rabe and C{\'e}sar S{\'a}nchez}, booktitle={The post}, year={2014} }

Hyperproperties, as introduced by Clarkson and Schneider, characterize the correctness of a computer program as a condition on its set of computation paths. Standard temporal logics can only refer to a single path at a time, and therefore cannot express many hyperproperties of interest, including noninterference and other important properties in security and coding theory. In this paper, we investigate an extension of temporal logic with explicit path variables. We show that the quantification…

## 204 Citations

### The linear-hyper-branching spectrum of temporal logics

- Computer Scienceit Inf. Technol.
- 2014

The extended spectrum of temporal logics has recently been extended with logics for the specification of hyperproperties by relating the new logics to the linear-branching spectrum of process equivalences.

### Team Semantics for the Specification and Verification of Hyperproperties

- Computer ScienceMFCS
- 2018

This work develops team semantics for Linear Temporal Logic to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties, and shows that LTL under team semantics is a viable alternative to HyperLTL.

### HyperPCTL: A Temporal Logic for Probabilistic Hyperproperties

- Computer Science, PhilosophyQEST
- 2018

The logic proposed in this paper, \HyperPCTL, adds explicit and simultaneous quantification over multiple traces to PCTL that allows expressing probabilistic hyperproperties.

### The Hierarchy of Hyperlogics

- Computer Science, Philosophy2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

It is shown that while HyperQPTL and HyperCTL* are both undecidable in general, formulas within their $\exists^{*}\forall^{*}$ fragments are decidable.

### Deciding Hyperproperties

- Computer ScienceCONCUR
- 2016

This paper shows that the satisfiability problem of HyperLTL is PSPACE-complete for alternationfree formulas (and, hence, no more expensive than LTL satisfiability), EXPSPACE- complete for ∃∀ formulas, and undecidable for ∀∃ formulas.

### A Temporal Logic for Asynchronous Hyperproperties

- Computer ScienceCAV
- 2021

An asynchronous variant of HyperLTL is proposed, and it is shown that the model-checking problem for this variant is undecidable, and a decidable fragment is identified which covers a rich set of formulas with practical applications.

### Model-Checking HyperLTL for Pushdown Systems

- Computer ScienceSPIN
- 2018

An algorithm that over-approximates the model-checking problem with an automata-theoretic approach is introduced and it is shown how these approximations can be used to check security policies.

### Verifying Hyperliveness

- Computer ScienceCAV
- 2019

This paper reduces existential quantification to strategic choice and shows that synthesis algorithms can be used to eliminate the existential quantifiers automatically and can be extended to reactive system synthesis, i.e., to automatically construct a reactive system that is guaranteed to satisfy a given HyperLTL formula.

### Propositional Dynamic Logic for Hyperproperties

- Computer ScienceCONCUR
- 2020

This paper introduces HyperPDL-Delta, an adaptation of the Propositional Dynamic Logic of Fischer and Ladner for hyperproperties, and shows that HyperPDl-Delta model checking is asymptotically not more expensive than HyperCTL* model checking, despite its vastly increased expressive power.

## References

SHOWING 1-10 OF 102 REFERENCES

### A Temporal Logic for Hyperproperties

- Computer Science, PhilosophyArXiv
- 2013

It is shown that the quantification over paths naturally subsumes other extensions of temporal Logic with operators for information flow and knowledge, and the model checking problem for temporal logic with path quantification is decidable.

### Model Checking Information Flow in Reactive Systems

- Computer ScienceVMCAI
- 2012

This paper proposes a natural integration of information flow properties into linear-time temporal logics (LTL), adding a new modal operator, the hide operator, expressing that the observable behavior of a system is independent of the valuations of a secret variable.

### Augmenting Branching Temporal Logics with Existential Quantification over Atomic Propositions

- Computer Science, PhilosophyJ. Log. Comput.
- 1995

This paper examines the complexity of the model-checking problem in the two semantics for the logics CTL and CTL* augmented with existential quantification over atomic propositions, and shows that while fixing the formula dramatically reduces model- checking complexity in the tree semantics, its influence on the structure semantics is poor.

### Complete Proof System for QPTL

- Philosophy, Computer ScienceJ. Log. Comput.
- 2002

The paper presents an axiomatic system for quantified propositional temporal logic (QPTL), which is propositionalporal logic equipped with quantification over propositions (Boolean variables) and its expressive power is strictly higher than that of the unquantified version (PTL).

### “Sometimes” and “not never” revisited: on branching versus linear time temporal logic

- PhilosophyJACM
- 1986

A language, CTL*, in which a universal or existential path quantifier can prefix an arbitrary linear time assertion, is defined and the expressive power of a number of sublanguages is compared.

### Incremental Hyperproperty Model Checking via Games

- Computer ScienceNordSec
- 2013

The notion of incremental hyperproperties IHPs is introduced, motivated by the observation that they have a clearer and more feasible verification methodology, and to show that verification is indeed feasible, a decidable IHP verification methodology via games is presented and evaluated.

### Model Checking on Trees with Path Equivalences

- Computer ScienceTACAS
- 2007

This work proposes to enrich such tree models with "jump-edges" that capture observational indistinguishability: for an agent a, an a-labeled edge is added between two nodes if the observable behaviors of the agent a along the paths to these nodes are identical.

### Information Flow Analysis in Logical Form

- Computer ScienceSAS
- 2004

We specify an information flow analysis for a simple imperative language, using a Hoare-like logic. The logic facilitates static checking of a larger class of programs than can be checked by extant…

### Decidability of Quantifed Propositional Branching Time Logics

- PhilosophyAustralian Joint Conference on Artificial Intelligence
- 2001

This work extends the branching temporal logics CTL and CTL* with quantified propositions and considers various semantic interpretations for the quantification, showing that some interpretations of quantification allow us to represent non-propositional properties of Kripke frames, such as the branching degree of trees.