Constraint-Based Synthesis of Coupling Proofs

Abstract

Abstract.Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for probabilistic programs. First, we present f -coupled postconditions, an abstraction describing two correlated program executions. Second, we show how properties of f -coupled postconditions can imply various probabilistic properties of the original programs. Third, we demonstrate how to reduce the proof-search problem to a purely logical synthesis problem of the form ∃f. ∀X. ϕ, making probabilistic reasoning unnecessary. We develop a prototype implementation to automatically build coupling proofs for probabilistic properties, including uniformity and independence of program expressions.

Symbolic Execution for Randomized Programs

“…There are also many domain-specific automated analyses for specific probabilistic properties, such as termination and resource analysis [Chatterjee et al 2016;Moosbrugger et al 2021;Wang et al 2021], accuracy Smith et al 2019], reliability [Carbin et al 2012], differential privacy [Albarghouthi and Hsu 2018b;Barthe et al 2021] and other relational properties [Albarghouthi and Hsu 2018a;Farina et al 2021], and long-run properties of probabilistic loops [Bartocci et al 2019[Bartocci et al , 2020. Our approach aims to create a general-purpose analysis.…”

Foundations of Probabilistic Programming

“…Other non-relational properties could benefit from a similar approach, especially in conjunction with more sophisticated program transformations in pRHL to relate different copies of the same sampling instruction. Albarghouthi and Hsu (2018a) consider how to automatically construct such coupling proofs by program synthesis and verification techniques.…”