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 fragment of HyperLTL, a prototype model checker has been implemented.Syntax. Let π be a trace variable from an infinite supply V of trace variables. Formulas of HyperLTL are defined by the following grammar:Connectives ∃ and ∀ are universal and existential trace quantifiers, read as "along some traces" and "along all traces." For example, ∀π 1 . ∀π 2 . ∃π 3 . ψ means that for all traces π 1 and π 2 , there exists another trace π 3 , such that ψ holds on those three traces. (Since branching-time logics also have explicit path quantifiers, it

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Abstract-We present a specification language and algorithms for the online and offline monitoring of synchronous systems including circuits and embedded systems. Such monitoring is useful not only for testing, but also under actual deployment. The specification language is simple and expressive; it can describe both correctness/failure assertions along with interesting statistical measures that are useful for system profiling and coverage analysis. The algorithm for online monitoring of queries in this language follows a partial evaluation strategy: it incrementally constructs output streams from input streams, while maintaining a store of partially evaluated expressions for forward references. We identify a class of specifications, characterized syntactically, for which the algorithm's memory requirement is independent of the length of the input streams. Being able to bound memory requirements is especially important in online monitoring of large input streams. We extend the concepts used in the online algorithm to construct an efficient offline monitoring algorithm for large traces.We have implemented our algorithm and applied it to two industrial systems, the PCI bus protocol and a memory controller. The results demonstrate that our algorithms are practical and that our specification language is sufficiently expressive to handle specifications of interest to industry.