RHLE: Modular Deductive Verification of Relational $$\forall \exists $$ Properties

Dickerson, Robert; Ye, Qianchuan; Delaware, Benjamin

doi:10.1007/978-3-031-21037-2_4

Cited by 7 publications

(9 citation statements)

References 34 publications

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“…RHLE [20] is a Hoare-style relational logic that has been recently proposed to verify ∀∃-relational properties, such as program refinement [28]. We call the special case of RHLE where all commands in a triple are the same Relational Universal Existential; we can formalize its triples as follows: Definition 14.…”

Section: Beyond Over-and Underapproximationmentioning

confidence: 99%

“…4) Other hyperproperties: RHLE [20] supports overapproximate and (a limited form of) underapproximate reasoning. In addition, it can establish ∀∃-hyperproperties, such as generalized non-interference (Sect.…”

Section: Related Workmentioning

confidence: 99%

“…We call such Hoare logics underapproximate. Recent work [20]- [22] has proposed Hoare logics that combine underapproximate and overapproximate reasoning.…”

Section: Introductionmentioning

confidence: 99%

“…The acronyms refer to the following. CHL: Cartesian Hoare Logic [13], HL: Hoare Logic [1], [23], IL: Incorrectness Logic [16] or Reverse Hoare Logic [15], InSec: Insecurity Logic [19], OL: Outcome Logic [21], RHL: Relational Hoare Logic [3], RHLE [20].…”

Section: Introductionmentioning

confidence: 99%

“…While RHLE[20] in principle can reason about the existence of executions, it is unclear how to express the existence for all numbers n 2. The conclusion also holds for bounded arithmetic on an actual machine since y could be any integer in [MIN INT , MAX INT ].…”

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confidence: 99%

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Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Dardinier¹,

Müller²

2023

Preprint

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Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (so-called trace properties, such as functional correctness). On the one hand, Hoare logic has been generalized to prove properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic), by proving the existence of (bad combinations of) executions. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre-and post-state for functional properties or pairs of pre-and post-states for non-interference.In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. The resulting logic is simple yet expressive: its judgments can express arbitrary trace-and hyperproperties over the terminating executions of a program. By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic. In fact, we prove that Hyper Hoare Logic subsumes the properties handled by numerous existing correctness and incorrectness logics, and can express hyperproperties that no existing Hoare logic can. We also prove that Hyper Hoare Logic is sound and complete. All our technical results have been proved in Isabelle/HOL.

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Section: Beyond Over-and Underapproximationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…We call such Hoare logics underapproximate. Recent work [20]- [22] has proposed Hoare logics that combine underapproximate and overapproximate reasoning.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Dardinier¹,

Müller²

2023

Preprint

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Software Verification of Hyperproperties Beyond k-Safety

Beutner

Finkbeiner

2022

Lecture Notes in Computer Science

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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 $$\forall ^k\exists ^l$$ ∀ k ∃ l -safety properties in infinite-state systems. A $$\forall ^k\exists ^l$$ ∀ k ∃ l -safety property stipulates that for any k traces, there existl traces such that the resulting $$k+l$$ k + l traces do not interact badly. This combination of universal and existential quantification enables us to express many properties beyond k-safety, including, for example, generalized non-interference or program refinement. Our method is based on a strategy-based instantiation of existential trace quantification combined with a program reduction, both in the context of a fixed predicate abstraction. Notably, our framework allows for mutual dependence of strategy and reduction.

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Automated Software Verification of Hyperliveness

Beutner

2024

Lecture Notes in Computer Science

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Hyperproperties relate multiple executions of a program and are commonly used to specify security and information-flow policies. Most existing work has focused on the verification of k-safety properties, i.e., properties that state that all k-tuples of execution traces satisfy a given property. In this paper, we study the automated verification of richer properties that combine universal and existential quantification over executions. Concretely, we consider $$\forall ^k\exists ^l$$ ∀ k ∃ l properties, which state that for all k executions, there exist l executions that, together, satisfy a property. This captures important non-k-safety requirements, including hyperliveness properties such as generalized non-interference, opacity, refinement, and robustness. We design an automated constraint-based algorithm for the verification of $$\forall ^k\exists ^l$$ ∀ k ∃ l properties. Our algorithm leverages a sound-and-complete program logic and a (parameterized) strongest postcondition computation. We implement our algorithm in a tool called and report on encouraging experimental results.

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RHLE: Modular Deductive Verification of Relational $$\forall \exists $$ Properties

Cited by 7 publications

References 34 publications

Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Software Verification of Hyperproperties Beyond k-Safety

Automated Software Verification of Hyperliveness

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