arXiv subjects

Marco Gaboardi

Publications and source records attributed to Marco Gaboardi.

At least 19 recordsLinked to original sources

arXiv2026

Program Analysis for Adaptive Data Analysis

Data analyses are usually designed to identify some property of the population from which the data are drawn, generalizing beyond the specific data sample. For this reason, data analyses are often designed to produce a low generalization error, so that the result of an analysis on sample data does not differ too much from the result one would achieve over the entire population. An adaptive data analysis can be seen as a process composed of multiple queries interrogating some data, where the choice of which query to run next may rely on the results of previous queries. The generalization error of each individual query can be controlled using well-established statistical techniques. However, when queries are arbitrarily composed, errors can propagate through the chain of queries and lead to high generalization error. To address this issue, several techniques guarantee bounds not only on single queries but also on composed analyses. The choice of technique often depends on the chain of queries that an adaptive data analysis can generate. In this work, we consider adaptive data analyses implemented as while-like programs and design a program analysis to help identify which technique to use to control their generalization errors. More specifically, we formalize the intuitive notion of adaptivity as a quantitative property of programs. Based on this definition, we design a program analysis for soundly approximating this quantity. The analysis represents the data analysis as a weighted dependency graph, where weights upper-bound how often variables can be reached, and uses a path-search strategy to upper-bound adaptivity. We implement our program analysis and show that it can analyze several concrete data analyses with different adaptivity structures.

cs.PL↗

arXiv2026

A Type-and-Effect System for Temporal Dependency Analysis of Render-based Reactive Programs

Reactive programming frameworks such as React allow developers to build interactive applications by declaratively specifying how outputs depend on changing inputs. Although this model makes it easy to reason about what an application computes, the temporal behavior of reactive programs remains difficult to understand and verify. Applications implicitly rely on timing assumptions buried in framework runtimes, leading to subtle bugs such as stale reads, transient inconsistencies, order-dependent behavior, and unintended feedback cycles. To address these challenges, this paper presents Willow, a core calculus for reactive programming inspired by React. Willow gives a time-aware operational semantics that models computation in terms of renders, the fundamental evaluation step in which components produce user interface descriptions, and pairs it with a novel type-and-effect system that statically tracks timing behavior as effects. A "next" modality expresses delays measured not only in renders but in any unit the host environment exposes--renders, network requests, or milliseconds. A family of modalities tracks the lifecycle of event handlers: when they are registered, when they fire, when pending events are canceled and when handlers are removed. A key insight is that the resulting effects form a temporal dependency graph, letting standard graph algorithms statically detect render cascades and inter-render loops that cause non-termination or performance degradation. We formalize Willow and prove preservation of the effect system with respect to the time-aware semantics. We also implement a prototype checker with automatic effect inference and evaluate it on representative reactive patterns such as debouncing, form inputs, and API-driven updates. Our results demonstrate that time-aware typing provides a practical foundation for reasoning about the temporal correctness of reactive programs.

cs.PL↗

arXiv2026

Leaf: An Instrumentation-based Dynamic Analysis Framework for Rust

This paper presents LEAF, an instrumentation-based dynamic analysis framework for Rust. Although Rust has grown rapidly in recent years, the landscape of program analysis tools for Rust is still in relatively early stages. One notable gap is the lack of a general-purpose dynamic analysis framework that can support different analysis tasks. LEAF aims to fill this gap by providing a Rust-native framework for analyzing Rust programs at runtime. Rust provides rich semantic information through its ownership model, type system, memory model, and compiler-level representation. Therefore, LEAF focuses on how to make this information available to dynamic analyses. In particular, LEAF captures MIR-level semantic information, augments it with runtime facts, and delivers it to analyses as an event stream through Dynamic MIR (DMIR), an event-driven programming interface. Through three substantial dynamic analyses -- a concolic executor, a Rust-specific sanitizer, and a control-flow tracer -- we demonstrate the practicality and expressiveness of LEAF. Our evaluation further shows that LEAF's compile-time and runtime overhead is meaningful but manageable.

cs.SE↗

arXiv2026

A Bayesian Approach to Membership Inference for Statistical Release

The membership inference problem for publicly released statistics from a private dataset is well-studied. When developing and formally analyzing attack strategies, however, the focus has been on attacks that model the population using only its marginals. In practice, these attacks can perform well on various populations, however most formal analysis is for populations that follow a product distribution. These strategies may fail to leverage useful information about the population that is important for understanding a realistic privacy threat. In this work, we explore the impact of providing an attacker with additional information about the attribute dependency structure of the population, motivated by examples where multiple parties may have access to similarly structured data, for example the US Census and the IRS. To model this scenario, we re-frame the membership inference problem with respect to a population represented as a Bayesian network (BN). We develop a framework based on Bayesian decision-making which can incorporate prior information about the population to launch more effective, specialized attacks. To evaluate our framework, we introduce a specific attack instantiation which computes the Bayesian posterior using a probabilistic program, and prove its equivalence to an optimal variant of the likelihood ratio test attack for two populations with strong attribute dependency. We implement our program in the Roulette probabilistic programming language and show experimentally that it outperforms the likelihood ratio test and inner product attacks on five commonly used BNs, where the population dependency structure is too complex for the existing attacks to be manually adapted.

cs.CR↗

arXiv2026

Separating Oblivious and Adaptive Differential Privacy under Continual Observation

We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm's output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an $(\varepsilon,0)$-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every $(\varepsilon,\delta)$-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.

cs.CR↗

arXiv2026

A Category-Theoretic Framework for Dependent Effect Systems

Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning about effectful computations. However, existing categorical frameworks for graded monads do not support effects that may depend on program values, which we call dependent effects, thereby limiting their expressiveness. We address this limitation by introducing indexed graded monads, a categorical generalization of graded monads inspired by the fibrational "indexed" view and by classical categorical semantics of dependent type theories. We show how indexed graded monads provide semantics for a refinement type system with dependent effects. We also show how this type system can be instantiated with specific choices of parameters to obtain several formal systems for reasoning about specific program properties. These instances include, in particular, cost analysis, probability-bound reasoning, expectation-bound reasoning, and temporal safety verification.

cs.LO↗

arXiv2026

Outrunning Big KATs: Efficient Decision Procedures for Variants of GKAT

This paper presents several efficient decision procedures for trace equivalence of GKAT automata, which make use of on-the-fly symbolic techniques via SAT solvers. To demonstrate applicability of our algorithms, we designed symbolic derivatives for CF-GKAT, a practical system based on GKAT designed to validate control-flow transformations. We implemented the algorithms in Rust and evaluated them on both randomly generated benchmarks and real-world control-flow transformations. Indeed, we observed order-of-magnitude performance improvements against existing implementations for both KAT and CF-GKAT. Notably, our experiments also revealed a bug in Ghidra, an industry-standard decompiler, highlighting the practical viability of these systems.

cs.PL↗

arXiv2025

Cryptis: Cryptographic Reasoning in Separation Logic

We introduce Cryptis, an extension of the Iris separation logic that can be used to verify cryptographic components using the symbolic model of cryptography. The combination of separation logic and cryptographic reasoning allows us to prove the correctness of a protocol and later reuse this result to verify larger systems that rely on the protocol. To make this integration possible, we propose novel specifications for authentication protocols that allow agents in a network to agree on the use of system resources. We evaluate our approach by verifying various authentication protocols and a key-value store server that uses these authentication protocols to connect to clients. Our results are formalized in Coq.

cs.CR↗

arXiv2024

Kleene algebra with commutativity conditions is undecidable

We prove that the equational theory of Kleene algebra with commutativity conditions on primitives (or atomic terms) is undecidable, thereby settling a longstanding open question in the theory of Kleene algebra. While this question has also been recently solved independently by Kuznetsov, our results hold even for weaker theories that do not support the induction axioms of Kleene algebra.

math.LO↗

arXiv2024

Finite-memory Strategies for Almost-sure Energy-MeanPayoff Objectives in MDPs

We consider finite-state Markov decision processes with the combined Energy-MeanPayoff objective. The controller tries to avoid running out of energy while simultaneously attaining a strictly positive mean payoff in a second dimension. We show that finite memory suffices for almost surely winning strategies for the Energy-MeanPayoff objective. This is in contrast to the closely related Energy-Parity objective, where almost surely winning strategies require infinite memory in general. We show that exponential memory is sufficient (even for deterministic strategies) and necessary (even for randomized strategies) for almost surely winning Energy-MeanPayoff. The upper bound holds even if the strictly positive mean payoff part of the objective is generalized to multidimensional strictly positive mean payoff. Finally, it is decidable in pseudo-polynomial time whether an almost surely winning strategy exists.

cs.GT↗

arXiv2024

Programming Frameworks for Differential Privacy

Many programming frameworks have been introduced to support the development of differentially private software applications. In this chapter, we survey some of the conceptual ideas underlying these frameworks in a way that we hope will be helpful for both practitioners and researchers. For practitioners, the survey can provide a starting point for understanding what features may be valuable when selecting a programming framework. For researchers, it can help organize existing work in a unified way and provide context for understanding new features in future frameworks.

cs.CR↗

arXiv2023

The Complexity of Verifying Boolean Programs as Differentially Private

We study the complexity of the problem of verifying differential privacy for while-like programs working over boolean values and making probabilistic choices. Programs in this class can be interpreted into finite-state discrete-time Markov Chains (DTMC). We show that the problem of deciding whether a program is differentially private for specific values of the privacy parameters is PSPACE-complete. To show that this problem is in PSPACE, we adapt classical results about computing hitting probabilities for DTMC. To show PSPACE-hardness we use a reduction from the problem of checking whether a program almost surely terminates or not. We also show that the problem of approximating the privacy parameters that a program provides is PSPACE-hard. Moreover, we investigate the complexity of similar problems also for several relaxations of differential privacy: R\'enyi differential privacy, concentrated differential privacy, and truncated concentrated differential privacy. For these notions, we consider gap-versions of the problem of deciding whether a program is private or not and we show that all of them are PSPACE-complete.

cs.CR↗

arXiv2023

Continual Release of Differentially Private Synthetic Data from Longitudinal Data Collections

Motivated by privacy concerns in long-term longitudinal studies in medical and social science research, we study the problem of continually releasing differentially private synthetic data from longitudinal data collections. We introduce a model where, in every time step, each individual reports a new data element, and the goal of the synthesizer is to incrementally update a synthetic dataset in a consistent way to capture a rich class of statistical properties. We give continual synthetic data generation algorithms that preserve two basic types of queries: fixed time window queries and cumulative time queries. We show nearly tight upper bounds on the error rates of these algorithms and demonstrate their empirical performance on realistically sized datasets from the U.S. Census Bureau's Survey of Income and Program Participation.

cs.DS↗

arXiv2023

A Formal Model for Secure Multiparty Computation

Although Secure Multiparty Computation (SMC) has seen considerable development in recent years, its use is challenging, resulting in complex code which obscures whether the security properties or correctness guarantees hold in practice. For this reason, several works have investigated the use of formal methods to provide guarantees for SMC systems. However, these approaches have been applied mostly to domain specific languages (DSL), neglecting general-purpose approaches. In this paper, we consider a formal model for an SMC system for annotated C programs. We choose C due to its popularity in the cryptographic community and being the only general-purpose language for which SMC compilers exist. Our formalization supports all key features of C -- including private-conditioned branching statements, mutable arrays (including out of bound array access), pointers to private data, etc. We use this formalization to characterize correctness and security properties of annotated C, with the latter being a form of non-interference on execution traces. We realize our formalism as an implementation in the PICCO SMC compiler and provide evaluation results on SMC programs written in C.

cs.PL↗

arXiv2023

Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization

The notion of replicable algorithms was introduced in Impagliazzo et al. [STOC '22] to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output with high probability when its randomness is fixed and it is run on a new i.i.d. sample drawn from the same distribution. Using replicable algorithms for data analysis can facilitate the verification of published results by ensuring that the results of an analysis will be the same with high probability, even when that analysis is performed on a new data set. In this work, we establish new connections and separations between replicability and standard notions of algorithmic stability. In particular, we give sample-efficient algorithmic reductions between perfect generalization, approximate differential privacy, and replicability for a broad class of statistical problems. Conversely, we show any such equivalence must break down computationally: there exist statistical problems that are easy under differential privacy, but that cannot be solved replicably without breaking public-key cryptography. Furthermore, these results are tight: our reductions are statistically optimal, and we show that any computational separation between DP and replicability must imply the existence of one-way functions. Our statistical reductions give a new algorithmic framework for translating between notions of stability, which we instantiate to answer several open questions in replicability and privacy. This includes giving sample-efficient replicable algorithms for various PAC learning, distribution estimation, and distribution testing problems, algorithmic amplification of $\delta$ in approximate DP, conversions from item-level to user-level privacy, and the existence of private agnostic-to-realizable learning reductions under structured distributions.

cs.LG↗

arXiv2023

Differentially Private Confidence Intervals for Proportions under Stratified Random Sampling

Confidence intervals are a fundamental tool for quantifying the uncertainty of parameters of interest. With the increase of data privacy awareness, developing a private version of confidence intervals has gained growing attention from both statisticians and computer scientists. Differential privacy is a state-of-the-art framework for analyzing privacy loss when releasing statistics computed from sensitive data. Recent work has been done around differentially private confidence intervals, yet to the best of our knowledge, rigorous methodologies on differentially private confidence intervals in the context of survey sampling have not been studied. In this paper, we propose three differentially private algorithms for constructing confidence intervals for proportions under stratified random sampling. We articulate two variants of differential privacy that make sense for data from stratified sampling designs, analyzing each of our algorithms within one of these two variants. We establish analytical privacy guarantees and asymptotic properties of the estimators. In addition, we conduct simulation studies to evaluate the proposed private confidence intervals, and two applications to the 1940 Census data are provided.

stat.ME↗

arXiv2022

Bunched Fuzz: Sensitivity for Vector Metrics

Program sensitivity measures the distance between the outputs of a program when run on two related inputs. This notion, which plays a key role in areas such as data privacy and optimization, has been the focus of several program analysis techniques introduced in recent years. Among the most successful ones, we can highlight type systems inspired by linear logic, as pioneered by Reed and Pierce in the Fuzz programming language. In Fuzz, each type is equipped with its own distance, and sensitivity analysis boils down to type checking. In particular, Fuzz features two product types, corresponding to two different notions of distance: the tensor product combines the distances of each component by adding them, while the with product takes their maximum. In this work, we show that these products can be generalized to arbitrary $L^p$ distances, metrics that are often used in privacy and optimization. The original Fuzz products, tensor and with, correspond to the special cases $L^1$ and $L^\infty$. To ease the handling of such products, we extend the Fuzz type system with bunches -- as in the logic of bunched implications -- where the distances of different groups of variables can be combined using different $L^p$ distances. We show that our extension can be used to reason about quantitative properties of probabilistic programs.

cs.PL↗

arXiv2021

A Separation Logic for Negative Dependence

Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence, a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic, rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes.

cs.PL↗