System requirements related to concepts like information flow, knowledge, and robustness cannot be judged in terms of individual system executions, but rather require an analysis of the relationship between multiple executions. Such requirements belong to the class of hyperproperties, which generalize classic trace properties to properties of sets of traces. During the past decade, a range of new specification logics has been introduced with the goal of providing a unified theory for reasoning about hyperproperties. This paper gives an overview on the current landscape of logics for the specification of hyperproperties and on algorithms for satisfiability checking, model checking, monitoring, and synthesis.
In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express quantitative dependencies between such executions. The standard temporal logics for probabilistic systems, i.e., PCTL and PCTL* can refer only to a single path at a time and, hence, cannot express many probabilistic hyperproperties of interest. The logic proposed in this paper, \HyperPCTL, adds explicit and simultaneous quantification over multiple traces to P…
Two new logics for verification of hyperproperties are proposed. Hyperproperties characterize security policies, such as noninterference, as a property of sets of computation paths. Standard temporal logics such as LTL, CTL, and CTL* can refer only to a single path at a time, hence cannot express many hyperproperties of interest. The logics proposed here, HyperLTL and HyperCTL*, add explicit and simultaneous quantification over multiple paths to LTL and to CTL*. This kind of quantification enables expression of hyperproperties. A model checking algorithm for the proposed logics is given. For a…
Hyperproperties are commonly used in computer security to define information-flow policies and other requirements that reason about the relationship between multiple computations. In this paper, we study a novel class of hyperproperties where the individual computation paths are chosen by the strategic choices of a coalition of agents in a multi-agent system. We introduce HyperATL*, an extension of computation tree logic with path variables and strategy quantifiers. HyperATL* can express strategic hyperproperties, such as that the scheduler in a concurrent system has a strategy to avoid inform…
Hyperproperties are properties that describe the correctness of a system as a relation between multiple executions. Hyperproperties generalize trace properties and include information-flow security requirements, like noninterference, as well as requirements like symmetry, partial observation, robustness, and fault tolerance. We initiate the study of the specification and verification of hyperproperties of Markov decision processes (MDPs). We introduce the temporal logic PHL (Probabilistic Hyper Logic), which extends classic probabilistic logics with quantification over schedulers and traces. P…
Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying asynchronous hyperproperties have been investigated. Though model checking of these logics is undecidable, useful decidable fragments have been identified with applications e.g. for asynchronous security analysis. In this paper, we address expressiveness and decidability issues of temporal logics for asynchronous hyperproperties. We compare the expressiveness of t…
Hyperproperties are properties of computational systems that require more than one trace to evaluate, e.g., many information-flow security and concurrency requirements. Where a trace property defines a set of traces, a hyperproperty defines a set of sets of traces. The temporal logics HyperLTL and HyperCTL* have been proposed to express hyperproperties. However, their semantics are synchronous in the sense that all traces proceed at the same speed and are evaluated at the same position. This precludes the use of these logics to analyze systems whose traces can proceed at different speeds and a…
We present RVHyper, a runtime verification tool for hyperproperties. Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other. Specifications are given as formulas in the temporal logic HyperLTL, which extends linear-time temporal logic (LTL) with trace quantifiers and trace variables. RVHyper processes execution traces sequentially until a violation of the specification is detected. In this case, a counter example, in the form of a set of traces, is returned. As an example application, we show how RVHyper can be used to detect…
We investigate the logical foundations of hyperproperties. Hyperproperties generalize trace properties, which are sets of traces, to sets of sets of traces. The most prominent application of hyperproperties is information flow security: information flow policies characterize the secrecy and integrity of a system by comparing two or more execution traces, for example by comparing the observations made by an external observer on execution traces that result from different values of a secret variable. In this paper, we establish the first connection between temporal logics for hyperproperties and…
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 over paths naturally subsumes other extensions of temporal logic with operators for information flow …
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 $\exists^*$, $\exists^*\forall^1$…
Information security properties of reactive systems like non-interference often require relating different executions of the system to each other and following them simultaneously. Such hyperproperties can also be useful in other contexts, e.g., when analysing properties of distributed systems like linearizability. Since common logics like LTL, CTL, or the modal mu-calculus cannot express hyperproperties, the hyperlogics HyperLTL and HyperCTL* were developed to cure this defect. However, these logics are not able to express arbitrary omega-regular properties. In this paper, we introduce HyperP…
In this article we study linear temporal logics with team semantics (TeamLTL) that are novel logics for defining hyperproperties. We define Kamp-type translations of these logics into fragments of first-order team logic and second-order logic. We also characterize the expressive power and the complexity of model-checking and satisfiability of team logic and second-order logic by relating them to second- and third-order arithmetic. Our results set in a larger context the recent results of Lück showing that the extension of TeamLTL by the Boolean negation is highly undecidable under the so-calle…
This paper presents an extension of the safety fragment of Hennessy-Milner Logic with recursion over sets of traces, in the spirit of Hyper-LTL. It then introduces a novel monitoring setup that employs circuit-like structures to combine verdicts from regular monitors. The main contribution of this study is the monitors and their semantics themselves, as well as a monitor-synthesis procedure from formulae in the logic that yields `circuit-like monitors' of this type that are sound and violation complete over a finite set of infinite traces.
We investigate the problem of controller synthesis for hyperproperties specified in the temporal logic HyperLTL. Hyperproperties are system properties that relate multiple execution traces. Hyperproperties can elegantly express information-flow policies like noninterference and observational determinism. The controller synthesis problem is to automatically design a controller for a plant that ensures satisfaction of a given specification in the presence of the environment or adversarial actions. We show that the controller synthesis problem is decidable for HyperLTL specifications and finite-s…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a synchronous variant of team semantics. We study basic properties of this new logic and classify the computational complexity of its satisfiability, path, and model checking problem. Further, we examine how extensions of these basic logics react on adding other atomic operators. Finally, we compare its expressivity to the one of HyperLTL, another recently intr…
We study the repair problem for hyperproperties specified in the temporal logic HyperLTL. Hyperproperties are system properties that relate multiple computation traces. This class of properties includes information flow policies like noninterference and observational determinism. The repair problem is to find, for a given Kripke structure, a substructure that satisfies a given specification. We show that the repair problem is decidable for HyperLTL specifications and finite-state Kripke structures. We provide a detailed complexity analysis for different fragments of HyperLTL and different syst…
Many important properties of cyber-physical systems (CPS) are defined upon the relationship between multiple executions simultaneously in continuous time. Examples include probabilistic fairness and sensitivity to modeling errors (i.e., parameters changes) for real-valued signals. These requirements can only be specified by hyperproperties. In this work, we focus on verifying probabilistic hyperproperties for CPS. To cover a wide range of modeling formalisms, we first propose a general model of probabilistic uncertain systems (PUSs) that unify commonly studied CPS models such as continuous-tim…
We develop model checking algorithms for Temporal Stream Logic (TSL) and Hyper Temporal Stream Logic (HyperTSL) modulo theories. TSL extends Linear Temporal Logic (LTL) with memory cells, functions and predicates, making it a convenient and expressive logic to reason over software and other systems with infinite data domains. HyperTSL further extends TSL to the specification of hyperproperties - properties that relate multiple system executions. As such, HyperTSL can express information flow policies like noninterference in software systems. We augment HyperTSL with theories, resulting in Hype…
Hyperproperties, like observational determinism or symmetry, cannot be expressed as properties of individual computation traces, because they describe a relation between multiple computation traces. HyperLTL is a temporal logic that captures such relations through trace variables, which are introduced through existential and universal trace quantifiers and can be used to refer to multiple computations at the same time. In this paper, we study the satisfiability problem of HyperLTL. We show that the problem is PSPACE-complete for alternation-free formulas (and, hence, no more expensive than LTL…
Verifying hyperproperties at runtime is a challenging problem as hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other. It is necessary to store previously seen traces, because every new incoming trace needs to be compatible with every run of the system observed so far. Furthermore, the new incoming trace poses requirements on future traces. In our monitoring approach, we focus on those requirements by rewriting a hyperproperty in the temporal logic HyperLTL to a Boolean constraint system. A hyperproperty is then violated by…
Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other and are thus not monitorable by tools that consider computations in isolation. We present the monitoring approach implemented in the latest version of RVHyper, a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic HyperLTL, which extends linear-time temporal logic (LTL) with trace quantifiers and trace variables. RVHyper processes execution traces sequentially until a violation of the specification is detecte…
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their decidability and relative expressiveness. The new logics have been obtained from standard logics with two principal extensions: temporal logics, like LTL and CTL$^*$, have been generalized to hyperproperties by adding variables for traces or paths. First-order and second-order logics, like monadic first-order logic of order and MSO, have been extended with the…
Hyperproperties are properties of sets of computation traces. In this paper, we study quantitative hyperproperties, which we define as hyperproperties that express a bound on the number of traces that may appear in a certain relation. For example, quantitative non-interference limits the amount of information about certain secret inputs that is leaked through the observable outputs of a system. Quantitative non-interference thus bounds the number of traces that have the same observable input but different observable output. We study quantitative hyperproperties in the setting of HyperLTL, a te…
Many types of attacks on confidentiality stem from the nondeterministic nature of the environment that computer programs operate in (e.g., schedulers and asynchronous communication channels). In this paper, we focus on verification of confidentiality in nondeterministic environments by reasoning about asynchronous hyperproperties. First, we generalize the temporal logic A-HLTL to allow nested trajectory quantification, where a trajectory determines how different execution traces may advance and stutter. We propose a bounded model checking algorithm for A-HLTL based on QBF-solving for a fragmen…
Temporal hyperproperties are system properties that relate multiple execution traces. For (finite-state) hardware, temporal hyperproperties are supported by model checking algorithms, and tools for general temporal logics like HyperLTL exist. For (infinite-state) software, 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 $\forall^k\exists^l$-safety properties in infinite-state systems. A $\fora…
Hyperproperties, such as non-interference and observational determinism, relate multiple system executions to each other. They are not expressible in standard temporal logics, like LTL, CTL, and CTL*, and thus cannot be monitored with standard runtime verification techniques. HyperLTL extends linear-time temporal logic (LTL) with explicit quantification over traces in order to express Hyperproperties. We investigate the runtime verification problem of HyperLTL formulas for three different input models: (1) The parallel model, where a fixed number of system executions is processed in parallel. …
A specification given as a formula in linear temporal logic (LTL) defines a system by its set of traces. However, certain features such as information flow security constraints are rather modeled as so-called hyperproperties, which are sets of sets of traces. One logical approach to this is team logic, which is a logical framework for the specification of dependence and independence of information. LTL with team semantics has recently been discovered as a logic for hyperproperties. We study the complexity theoretic aspects of LTL with so-called synchronous team semantics and Boolean negation, …
An enforcement mechanism monitors a reactive system for undesired behavior at runtime and corrects the system's output in case it violates the given specification. In this paper, we study the enforcement problem for hyperproperties, i.e., properties that relate multiple computation traces to each other. We elaborate the notion of sound and transparent enforcement mechanisms for hyperproperties in two trace input models: 1) the parallel trace input model, where the number of traces is known a-priori and all traces are produced and processed in parallel and 2) the sequential trace input model, w…
Hyperproperties generalize trace properties by expressing relations between multiple computations. Hyperpropertes include policies from information-flow security, like observational determinism or non-interference, and many other system properties including promptness and knowledge. In this paper, we give an overview on the model checking problem for temporal hyperlogics. Our starting point is the model checking algorithm for HyperLTL, a reduction to Büchi automata emptiness. This basic construction can be extended with propositional quantification, resulting in an algorithm for HyperQPTL. It …
Hyperproperties are properties that refer to multiple computation traces. This includes many information-flow security policies, such as observational determinism, (generalized) noninterference, and noninference, and other system properties like symmetry or Hamming distances between in error-resistant codes. We introduce MGHyper, a tool for automatic satisfiability checking and model generation for hyperproperties expressed in HyperLTL. Unlike previous satisfiability checkers, MGHyper is not limited to the decidable $\exists^* \forall^*$ fragment of HyperLTL, but provides a semi-decisionproced…
Hyperproperties are a modern specification paradigm that extends trace properties to express properties of sets of traces. Temporal logics for hyperproperties studied in the literature, including HyperLTL, assume a synchronous semantics and enjoy a decidable model checking problem. In this paper, we introduce two asynchronous and orthogonal extensions of HyperLTL, namely Stuttering HyperLTL (HyperLTLS) and Context HyperLTL (HyperLTLC). Both of these extensions are useful, for instance, to formulate asynchronous variants of information-flow security properties. We show that for these logics, mo…
Bounded model checking (BMC) is an effective technique for hunting bugs by incrementally exploring the state space of a system. To reason about infinite traces through a finite structure and to ultimately obtain completeness, BMC incorporates loop conditions that revisit previously observed states. This paper focuses on developing loop conditions for BMC of HyperLTL- a temporal logic for hyperproperties that allows expressing important policies for security and consistency in concurrent systems, etc. Loop conditions for HyperLTL are more complicated than for LTL, as different traces may loop i…
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 canon…
University of Tübingen（蒂宾根大学）；Institut für Theoretische Informatik, Leibniz Universität Hannover（汉诺威莱布尼茨大学理论计算机科学研究所）；School of Computing Science, University of Glasgow（格拉斯哥大学计算科学学院）；Department of Computer Science, Aalborg University（奥尔堡大学计算机系）
We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic \HyperPCTL, which has been previously introduced for discrete-time Markov chains, to enable the specification of hyperproperties also for Markov decision processes. We generalize HyperPCTL by allowing explicit and simultaneous quantification over schedulers and probabilistic computation trees and show that it can express important quantitative requirements in security and privacy. We show that HyperPCTL model checking over MDPs is in gener…
Hyperproperties relate multiple computation traces to each other. Model checkers for hyperproperties thus return, in case a system model violates the specification, a set of traces as a counterexample. Fixing the erroneous relations between traces in the system that led to the counterexample is a difficult manual effort that highly benefits from additional explanations. In this paper, we present an explanation method for counterexamples to hyperproperties described in the specification logic HyperLTL. We extend Halpern and Pearl's definition of actual causality to sets of traces witnessing the…
We study the expressivity and complexity of model checking linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking re…
We study satisfiability for HyperLTL with a $\forall^*\exists^*$ quantifier prefix, known to be highly undecidable in general. HyperLTL can express system properties that relate multiple traces (so-called hyperproperties), which are often combined with trace properties that specify functional behavior on single traces. Following this conceptual split, we first define several safety and liveness fragments of $\forall^*\exists^*$ HyperLTL, and characterize the complexity of their (often much easier) satisfiability problem. We then add LTL trace properties as functional specifications. Though (hi…
