arXiv subjects

Kwing Hei Li

Publications and source records attributed to Kwing Hei Li.

11 recordsLinked to original sources

arXiv2026

Elton: Urn Resources for Reasoning about Adversarial Probabilistic Programs

Probabilistic programs are important for many applications. For security applications in particular, one is interested in establishing properties that hold in the presence of arbitrary adversaries, i.e., unknown pieces of code. We present Elton, a higher-order separation logic for reasoning about higher-order probabilistic programs utilizing unknown adversarial code. Elton incorporates novel logical facilities for specifying invariants over distributional properties using delayed samplings at the language level, and a new kind of separation-logic predicate called urn resources at the logic level. We show that these extensions are sound and can be erased back to a standard call-by-value semantics. Combined with other features, e.g. invariants and ghost resources, Elton is expressive enough to prove error bounds on a wide range of security examples, some of which are beyond the scope of previous techniques. All proofs are mechanized with the Rocq proof assistant and the Iris separation logic framework.

cs.LO↗

arXiv2026

Verifying Exact Samplers for Continuous Distributions with a Discrete Program Logic

Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in algorithms for differential privacy. An alternative is to use exact sampling algorithms based on computable reals, which can lazily generate the digits of a continuous sample to arbitrary precision. However, these algorithms are intricate, and implementing and using them involves a combination of semantically challenging language features, such as probabilistic choice, higher-order functions, and dynamically-allocated mutable state. In this paper we present Continuous-Eris, a higher-order separation logic for verifying the correctness of exact sampling algorithms for computable distributions. To demonstrate Continuous-Eris, we verify the correctness of computable samplers for the uniform, Gaussian, and Laplace distributions, as well as a library for exact real arithmetic for working with generated samples. All of the results in this paper have been verified in the Rocq proof assistant.

cs.LO↗

arXiv2026

Contextual Refinement of Higher-Order Concurrent Probabilistic Programs (Extended Version)

We present Foxtrot, the first higher-order separation logic for proving contextual refinement of higher-order concurrent probabilistic programs with higher-order local state. From a high level, Foxtrot inherits various concurrency reasoning principles from standard concurrent separation logic, e.g. invariants and ghost resources, and supports advanced probabilistic reasoning principles for reasoning about complex probability distributions induced by concurrent threads, e.g. tape presampling and induction by error amplification. The integration of these strong reasoning principles is highly non-trivial due to the combination of probability and concurrency in the language and the complexity of the Foxtrot model; the soundness of the logic relies on a version of the axiom of choice within the Iris logic, which is not used in earlier work on Iris-based logics. We demonstrate the expressiveness of Foxtrot on a wide range of examples, including the adversarial von Neumann coin and the $\mathsf{randombytes\_uniform}$ function of the Sodium cryptography software library. All results have been mechanized in the Rocq proof assistant and the Iris separation logic framework.

cs.LO↗

arXiv2026

Modular Verification of Differential Privacy in Probabilistic Higher-Order Separation Logic (Extended Version)

Differential privacy is the standard method for privacy-preserving data analysis. The importance of having strong guarantees on the reliability of implementations of differentially private algorithms is widely recognized and has sparked fruitful research on formal methods. However, the design patterns and language features used in modern DP libraries as well as the classes of guarantees that the library designers wish to establish often fall outside of the scope of previous verification approaches. We introduce a program logic suitable for verifying differentially private implementations written in complex, general-purpose programming languages. Our logic has first-class support for reasoning about privacy budgets as a separation logic resource. The expressiveness of the logic and the target language allow our approach to handle common programming patterns used in the implementation of libraries for differential privacy, such as privacy filters and caching. While previous work has focused on developing guarantees for programs written in domain-specific languages or for privacy mechanisms in isolation, our logic can reason modularly about primitives, higher-order combinators, and interactive algorithms. We demonstrate the applicability of our approach by implementing a verified library of differential privacy mechanisms, including an online version of the Sparse Vector Technique, as well as a privacy filter inspired by the popular Python library OpenDP, which crucially relies on our ability to handle the combination of randomization, local state, and higher-order functions. We demonstrate that our specifications are general and reusable by instantiating them to verify clients of our library. All of our results have been foundationally verified in the Rocq Prover.

cs.PL↗

arXiv2025

Modular Reasoning about Error Bounds for Concurrent Probabilistic Programs (Extended Version)

We present Coneris, the first higher-order concurrent separation logic for reasoning about error probability bounds of higher-order concurrent probabilistic programs with higher-order state. To support modular reasoning about concurrent (non-probabilistic) program modules, state-of-the-art program logics internalize the classic notion of linearizability within the logic through the concept of logical atomicity. Coneris extends this idea to probabilistic concurrent program modules. Thus Coneris supports modular reasoning about probabilistic concurrent modules by capturing a novel notion of randomized logical atomicity within the logic. To do so, Coneris utilizes presampling tapes and a novel probabilistic update modality to describe how state is changed probabilistically at linearization points. We demonstrate this approach by means of smaller synthetic examples and larger case studies. All of the presented results, including the meta-theory, have been mechanized in the Rocq proof assistant and the Iris separation logic framework This is the extended version of the same paper accepted at ICFP 2025, where more details of proofs and case studies are included in the Appendix.

cs.LO↗

arXiv2024

Approximate Relational Reasoning for Higher-Order Probabilistic Programs

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 approximate equivalences of probabilistic programs. However, existing approximate relational logics are mostly restricted to first-order programs without general state. In this paper we develop Approxis, a higher-order approximate relational separation logic for reasoning about approximate equivalence of programs written in an expressive ML-like language with discrete probabilistic sampling, higher-order functions, and higher-order state. The Approxis logic recasts the concept of error credits in the relational setting to reason about relational approximation, which allows for expressive notions of modularity and composition, a range of new approximate relational rules, and an internalization of a standard limiting argument for showing exact probabilistic equivalences by approximation. We also use Approxis to develop a logical relation model that quantifies over error credits, which can be used to prove exact contextual equivalence. We demonstrate the flexibility of our approach on a range of examples, including the PRP/PRF switching lemma, IND\$-CPA security of an encryption scheme, and a collection of rejection samplers. All of the results have been mechanized in the Coq proof assistant and the Iris separation logic framework.

cs.LO↗

arXiv2024

Error Credits: Resourceful Reasoning about Error Bounds for Higher-Order Probabilistic Programs

Probabilistic programs often trade accuracy for efficiency, and thus may, with a small probability, return an incorrect result. It is important to obtain precise bounds for the probability of these errors, but existing verification approaches have limitations that lead to error probability bounds that are excessively coarse, or only apply to first-order programs. In this paper we present Eris, a higher-order separation logic for proving error probability bounds for probabilistic programs written in an expressive higher-order language. Our key novelty is the introduction of error credits, a separation logic resource that tracks an upper bound on the probability that a program returns an erroneous result. By representing error bounds as a resource, we recover the benefits of separation logic, including compositionality, modularity, and dependency between errors and program terms, allowing for more precise specifications. Moreover, we enable novel reasoning principles such as expectation-preserving error composition, amortized error reasoning, and error induction. We illustrate the advantages of our approach by proving amortized error bounds on a range of examples, including collision probabilities in hash functions, which allow us to write more modular specifications for data structures that use them as clients. We also use our logic to prove correctness and almost-sure termination of rejection sampling algorithms. All of our results have been mechanized in the Coq proof assistant using the Iris separation logic framework and the Coquelicot real analysis library.

cs.LO↗

arXiv2024

Tachis: Higher-Order Separation Logic with Credits for Expected Costs

We present Tachis, a higher-order separation logic to reason about the expected cost of probabilistic programs. Inspired by the uses of time credits for reasoning about the running time of deterministic programs, we introduce a novel notion of probabilistic cost credit. Probabilistic cost credits are a separation logic resource that can be used to pay for the cost of operations in programs, and that can be distributed across all possible branches of sampling instructions according to their weight, thus enabling us to reason about expected cost. The representation of cost credits as separation logic resources gives Tachis a great deal of flexibility and expressivity. In particular, it permits reasoning about amortized expected cost by storing excess credits as potential into data structures to pay for future operations. Tachis further supports a range of cost models, including running time and entropy usage. We showcase the versatility of this approach by applying our techniques to prove upper bounds on the expected cost of a variety of probabilistic algorithms and data structures, including randomized quicksort, hash tables, and meldable heaps. All of our results have been mechanized using Coq, Iris, and the Coquelicot real analysis library.

cs.LO↗

arXiv2022

Formalizing May's Theorem

This report presents a formalization of May's theorem in the proof assistant Coq. It describes how the theorem statement is first translated into Coq definitions, and how it is subsequently proved. Various aspects of the proof and related work are discussed. To the best of the author's knowledge, this project is the first documented attempt in mechanizing May's Theorem.

cs.LO↗

arXiv2022

Secure Aggregation for Federated Learning in Flower

Federated Learning (FL) allows parties to learn a shared prediction model by delegating the training computation to clients and aggregating all the separately trained models on the server. To prevent private information being inferred from local models, Secure Aggregation (SA) protocols are used to ensure that the server is unable to inspect individual trained models as it aggregates them. However, current implementations of SA in FL frameworks have limitations, including vulnerability to client dropouts or configuration difficulties. In this paper, we present Salvia, an implementation of SA for Python users in the Flower FL framework. Based on the SecAgg(+) protocols for a semi-honest threat model, Salvia is robust against client dropouts and exposes a flexible and easy-to-use API that is compatible with various machine learning frameworks. We show that Salvia's experimental performance is consistent with SecAgg(+)'s theoretical computation and communication complexities.

cs.LG↗

arXiv2022

Flower: A Friendly Federated Learning Research Framework

Federated Learning (FL) has emerged as a promising technique for edge devices to collaboratively learn a shared prediction model, while keeping their training data on the device, thereby decoupling the ability to do machine learning from the need to store the data in the cloud. However, FL is difficult to implement realistically, both in terms of scale and systems heterogeneity. Although there are a number of research frameworks available to simulate FL algorithms, they do not support the study of scalable FL workloads on heterogeneous edge devices. In this paper, we present Flower -- a comprehensive FL framework that distinguishes itself from existing platforms by offering new facilities to execute large-scale FL experiments and consider richly heterogeneous FL device scenarios. Our experiments show Flower can perform FL experiments up to 15M in client size using only a pair of high-end GPUs. Researchers can then seamlessly migrate experiments to real devices to examine other parts of the design space. We believe Flower provides the community with a critical new tool for FL study and development.

cs.LG↗