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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…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
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…
We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate…
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…
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…
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 Hoare logic (PHL) is an extension of Hoare logic and is specifically useful in verifying randomized programs. It allows researchers to formally reason about the behavior of programs with stochastic elements, ensuring the…
We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…
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…
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…
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…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Hoare-style program logics are a popular and effective technique for software verification. Relational program logics are an instance of this approach that enables reasoning about relationships between the execution of two or more programs.…
Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant…
As Large Language Models (LLMs) become increasingly embedded in empirical research workflows, their use as analytical tools for quantitative or qualitative data raises pressing concerns for scientific integrity. This opinion paper draws a…
Research on deductive verification of probabilistic programs has considered expectation-based logics, where pre- and post-conditions are real-valued functions on states, and assertion-based logics, where pre- and post-conditions are boolean…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…