Related papers: Probabilistic Couplings for Probabilistic Reasonin…
Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by…
In this paper, we develop compositional methods for formally verifying differential privacy for algorithms whose analysis goes beyond the composition theorem. Our methods are based on the observation that differential privacy has deep…
Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a…
Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings…
Differential privacy is a promising formal approach to data privacy, which provides a quantitative bound on the privacy cost of an algorithm that operates on sensitive information. Several tools have been developed for the formal…
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…
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…
Differential privacy has emerged as a promising probabilistic formulation of privacy, generating intense interest within academia and industry. We present a push-button, automated technique for verifying $\varepsilon$-differential privacy…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules…
Approximate relational Hoare logic (apRHL) is a logic for formal verification of the differential privacy of databases written in the programming language pWHILE. Strictly speaking, however, this logic deals only with discrete random…
Differential privacy is a rigorous, worst-case notion of privacy-preserving computation. Informally, a probabilistic program is differentially private if the participation of a single individual in the input database has a limited effect on…
We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of…
Program sensitivity, also known as Lipschitz continuity, describes how small changes in a program's input lead to bounded changes in the output. We propose an average notion of program sensitivity for probabilistic programs---expected…
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
We present a logic for reasoning about pairs of interactive quantum programs - quantum relational Hoare logic (qRHL). This logic follows the spirit of probabilistic relational Hoare logic (Barthe et al. 2009) and allows us to formulate how…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…