Unifying Hyper and Epistemic Temporal Logics

Bozzelli, Laura; Maubert, Bastien; Pinchinat, Sophie

doi:10.1007/978-3-662-46678-0_11

Cited by 27 publications

(22 citation statements)

References 29 publications

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“…Let a PCP instance with Σ = {a 1 , a 2 , ..., a n } and two lists α and β be given. We choose our set of atomic propositions as follows: AP := I∪ O with I := {i} and O := (Σ ∪ {ȧ 1 ,ȧ 2 , ...,ȧ n } ∪ #) 2 , where we use the dot symbol to encode that a stone starts at this position of the trace. We writeã to denote either a orȧ.…”

Section: Theorem 4 Realizability Is Undecidable For Hyperqptl Formulmentioning

confidence: 99%

“…Promptness is a property stating that there is a bound b , common for all traces, on the number of steps up to which an event e must have happened. Additionally, just like LTL, HyperLTL can express neither -regular nor epistemic properties [ 2 , 29 ]. Epistemic properties are statements about the transfer of knowledge between several components.…”

Section: Introductionmentioning

confidence: 99%

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Realizing $$\omega $$-regular Hyperproperties

Finkbeiner¹,

Hahn²,

Hofmann³

et al. 2020

Computer Aided Verification

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We study the expressiveness and reactive synthesis problem of HyperQPTL, a logic that specifies ω-regular hyperproperties. HyperQPTL is an extension of linear-time temporal logic (LTL) with explicit trace and propositional quantification and therefore truly combines trace relations and ω-regularity. As such, HyperQPTL can express promptness, which states that there is a common bound on the number of steps up to which an event must have happened. We demonstrate how the HyperQPTL formulation of promptness differs from the type of promptness expressible in the logic Prompt-LTL. Furthermore, we study the realizability problem of HyperQPTL by identifying decidable fragments, where one decidable fragment contains formulas for promptness. We show that, in contrast to the satisfiability problem of HyperQPTL, propositional quantification has an immediate impact on the decidability of the realizability problem. We present a reduction to the realizability problem of HyperLTL, which immediately yields a bounded synthesis procedure. We implemented the synthesis procedure for HyperQPTL in the bounded synthesis tool BoSy. Our experimental results show that a range of arbiter satisfying promptness can be synthesized.

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Section: Theorem 4 Realizability Is Undecidable For Hyperqptl Formulmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Realizing $$\omega $$-regular Hyperproperties

Finkbeiner¹,

Hahn²,

Hofmann³

et al. 2020

Computer Aided Verification

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show abstract

“…It states that the set of traces can be partitioned into two parts, one where eventually a determines the value of b, and another where eventually c determines the value of d. A system satisfying this property can have some unobserved input that influences the dependency of some of its variables. The property is not expressible in HyperLTL, because HyperLTL cannot state the property "there is a point in time at which p holds on all (or infinitely many) traces" [2].…”

Section: Definition 15 (The Left-flat Fragment) Let a Be A Collection...mentioning

confidence: 99%

Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity

Virtema¹,

Hofmann²,

Finkbeiner³

et al. 2020

Preprint

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We study the expressivity and the model checking problem of linear temporal logic with team semantics (TeamLTL). In contrast to LTL, TeamLTL is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. Logics for hyperproperties have so far been mostly obtained by extending temporal logics like LTL and QPTL with trace quantification, resulting in HyperLTL and HyperQPTL. We study the expressiveness of TeamLTL (and its extensions with downward closed generalised atoms A and connectives such as Boolean disjunction ) in comparison to HyperLTL and HyperQPTL. Thereby, we also obtain a number of model checking results for TeamLTL, a question which is so far an open problem. The two types of logics follow a fundamentally different approach to hyperproperties and are are of incomparable expressiveness. We establish that the universally quantified fragment of HyperLTL subsumes the so-called k-coherent fragment of TeamLTL(A, ). This also implies that the model checking problem is decidable for the fragment. We show decidability of model checking of the so-called left-flat fragment of TeamLTL(A, ) via a translation to a decidable fragment of HyperQPTL. Finally, we show that the model checking problem of TeamLTL with Boolean disjunction and inclusion atom is undecidable.

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“…Since MPL [E] and MSO [E] are branching time logics while is a linear time logic, just like FOL [<,E] and S1S [E], we restrict our further analysis to the relationship between and these latter two logics. We believe that the expressive power of FOL [<,E] and is incomparable: As for HyperLTL [Bozzelli et al 2015], the property that an atomic proposition does not occur on a certain level in the tree (of traces) ś which is directly expressible in FOL [<,E] ś likely is not expressible in . On the other hand, for singleton trace sets, and FOL [<,E] degenerate to the linear time -calculus and FOL [<], respectively, and it is known that FOL[<] -unlike the linear time -calculus -cannot express all -regular properties.…”

Section: Introductionmentioning

confidence: 99%

Automata and fixpoints for asynchronous hyperproperties

Gutsfeld

Müller-Olm

Ohrem

2021

Proc. ACM Program. Lang.

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Hyperproperties have received increasing attention in the last decade due to their importance e.g. for security analyses. Past approaches have focussed on synchronous analyses, i.e. techniques in which different paths are compared lockstepwise. In this paper, we systematically study asynchronous analyses for hyperproperties by introducing both a novel automata model (Alternating Asynchronous Parity Automata) and the temporal fixpoint calculus H µ , the first fixpoint calculus that can systematically express hyperproperties in an asynchronous manner and at the same time subsumes the existing logic HyperLTL. We show that the expressive power of both models coincides over fixed path assignments. The high expressive power of both models is evidenced by the fact that decision problems of interest are highly undecidable, i.e. not even arithmetical. As a remedy, we propose approximative analyses for both models that also induce natural decidable fragments.

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Unifying Hyper and Epistemic Temporal Logics

Cited by 27 publications

References 29 publications

Realizing $$\omega $$-regular Hyperproperties

Realizing $$\omega $$-regular Hyperproperties

Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity

Automata and fixpoints for asynchronous hyperproperties

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