Constraint-Based Synthesis of Coupling Proofs [article]

Aws Albarghouthi, Justin Hsu
2018 arXiv   pre-print
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.
more » ... d, we demonstrate how to reduce the proof-search problem to a purely logical synthesis problem of the form ∃ f∀ Xϕ, making probabilistic reasoning unnecessary. We develop a prototype implementation to automatically build coupling proofs for probabilistic properties, including uniformity and independence of program expressions.
arXiv:1804.04052v1 fatcat:voa5gdpbrbbhhgydfyc7olp6bm