311 research outputs found
A Temporal Logic for Hyperproperties
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 and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
Second-Order Hyperproperties
We introduce HyperLTL, a temporal logic for the specification of
hyperproperties that allows for second-order quantification over sets of
traces. Unlike first-order temporal logics for hyperproperties, such as
HyperLTL, HyperLTL can express complex epistemic properties like common
knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The
model checking problem of HyperLTL is, in general, undecidable. For the
expressive fragment where second-order quantification is restricted to smallest
and largest sets, we present an approximate model-checking algorithm that
computes increasingly precise under- and overapproximations of the quantified
sets, based on fixpoint iteration and automata learning. We report on
encouraging experimental results with our model-checking algorithm, which we
implemented in the tool~\texttt{HySO}
On the Expressive Power of TeamLTL and First-Order Team Logic over Hyperproperties
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 Luck showing that the extension of TeamLTL by the Boolean negation is highly undecidable under the so-called synchronous semantics. We also study stutter-invariant fragments of extensions of TeamLTL.Peer reviewe
The Hierarchy of Hyperlogics
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
equal-level predicate. We study the impact of the two extensions across the
spectrum of linear-time and branching-time logics, in particular for logics
with quantification over propositions. The resulting hierarchy of hyperlogics
differs significantly from the classical hierarchy, suggesting that the
equal-level predicate adds more expressiveness than trace and path variables.
Within the hierarchy of hyperlogics, we identify new boundaries on the
decidability of the satisfiability problem. Specifically, we show that while
HyperQPTL and HyperCTL are both undecidable in general, formulas within
their fragments are decidable.Comment: Originally published at LICS 201
Second-Order Hyperproperties
We introduce Hyper^2LTL, a temporal logic for the specification of hyperproperties that allows for second-order quantification over sets of traces. Unlike first-order temporal logics for hyperproperties, such as HyperLTL, Hyper^2LTL can express complex epistemic properties like common knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The model checking problem of Hyper^2LTL is, in general, undecidable. For the expressive fragment where second-order quantification is restricted to smallest and largest sets, we present an approximate model-checking algorithm that computes increasingly precise under- and overapproximations of the quantified sets, based on fixpoint iteration and automata learning. We report on encouraging experimental results with our model-checking algorithm, which we implemented in the tool HySO
Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties
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 these logics together with the extension S1S[E] of S1S with the equal-level predicate by obtaining an almost complete expressiveness picture. We also study the expressive power of these logics when interpreted on singleton sets of traces. We show that for two asynchronous extensions of HyperLTL, checking the existence of a singleton model is already undecidable, and for one of them, namely Context HyperLTL (HyperLTL_C), we establish a characterization of the singleton models in terms of the extension of standard FO[<] over traces with addition. This last result generalizes the well-known equivalence between FO[<] and LTL. Finally, we identify new boundaries on the decidability of model checking HyperLTL_C
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