Quantitative Weakest Hyper Pre: Unifying Correctness and Incorrectness Hyperproperties via Predicate Transformers

We present a novel weakest pre calculus for reasoning about quantitative hyperproperties over nondeterministic and probabilistic programs. Whereas existing calculi allow reasoning about the expected value that a quantity assumes after program termination from a single initial state, we do so for ini...

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Bibliographic Details
Published in:Proceedings of ACM on programming languages Vol. 8; no. OOPSLA2; pp. 817 - 845
Main Authors: Zhang, Linpeng, Zilberstein, Noam, Kaminski, Benjamin Lucien, Silva, Alexandra
Format: Journal Article
Language:English
Published: New York, NY, USA ACM 08.10.2024
Subjects:
Axiomatic semantics
Hoare logic
Logic and verification
Pre- and post-conditions
Probabilistic computation
Program analysis
Program verification
Programming logic
Theory of computation
weakest precondition
strongest postcondition
hyperproperties
probabilistic verification
quantitative software verification
nondeterminism
ISSN:2475-1421, 2475-1421
Online Access:Get full text
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Summary:We present a novel weakest pre calculus for reasoning about quantitative hyperproperties over nondeterministic and probabilistic programs. Whereas existing calculi allow reasoning about the expected value that a quantity assumes after program termination from a single initial state, we do so for initial sets of states or initial probability distributions. We thus (i) obtain a weakest pre calculus for hyper Hoare logic and (ii) enable reasoning about so-called hyperquantities which include expected values but also quantities (e.g. variance) out of scope of previous work. As a byproduct, we obtain a novel strongest post for weighted programs that extends both existing strongest and strongest liberal post calculi. Our framework reveals novel dualities between forward and backward transformers, correctness and incorrectness, as well as nontermination and unreachability.
ISSN:2475-1421
2475-1421
DOI:10.1145/3689740