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A Quantitative Probabilistic Relational Hoare Logic

Authors: Avanzini, Martin; Barthe, Gilles; Davoli, Davide; Grégoire, Benjamin;

A Quantitative Probabilistic Relational Hoare Logic

Abstract

We introduce eRHL, a program logic for reasoning about relational expectation properties of pairs of probabilistic programs. eRHL is quantitative, i.e., its pre- and post-conditions take values in the extended non-negative reals. Thanks to its quantitative assertions, eRHL overcomes randomness alignment restrictions from prior logics, including pRHL, a popular relational program logic used to reason about security of cryptographic constructions, and apRHL, a variant of pRHL for differential privacy. As a result, eRHL is the first relational probabilistic program logic to be supported by non-trivial soundness and completeness results for all almost surely terminating programs. We show that eRHL is sound and complete with respect to program equivalence, statistical distance, and differential privacy. We also show that every pRHL judgment is valid iff it is provable in eRHL. We showcase the practical benefits of eRHL with examples that are beyond reach of pRHL and apRHL.

Country
France
Keywords

FOS: Computer and information sciences, Computer Science - Logic in Computer Science, probabilistic programs, Hoare logic, [INFO] Computer Science [cs], formal verification, Logic in Computer Science (cs.LO)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
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