Interactive Verification Paradigm for Data Attribution

• The paper introduces formal and mechanizable methods for verifying data attribution and privacy using interactive, modular proofs.
• It employs differential noninterference and algorithmic unwinding techniques to rigorously bound privacy leakage in interactive systems.
• The approach enables scalable, compositional verification via automated checks, ensuring robust, auditable data handling across subsystems.

An interactive verification paradigm for data attribution introduces formal and mechanizable methods by which the properties of data use—such as privacy guarantees, responsible handling, and provenance—can be rigorously analyzed and certified within interactive or dynamic systems. Rather than relying solely on global, batch-style proofs or informal practices, this paradigm leverages formal models, local reasoning principles, algorithmic unwinding techniques, and mechanical checks to provide modular, scalable, and incrementally composable verification of system behavior with respect to data handling. This approach underpins new ways to establish, audit, and compose evidence of properties such as differential privacy, noninterference, and bounded information leakage in complex interactive systems.

1. Formal Modeling of Interactive Systems

A central tenet is the precise modeling of interactive data systems as probabilistic transition systems (automata) that delineate clearly between input actions (e.g., data submissions, queries) and output actions (e.g., responses, observable events), as well as between internal (hidden or administrative) transitions and externally visible operations. This model supports rigorous tracking of state evolution and attribution of actions to specific data points.

A formal state machine is constructed such that:

• States encapsulate all information relevant to privacy/data attribution at a given time.
• Transitions are annotated with their type (input, output, or internal/hidden).
• Sequences of visible outputs (traces) can be used as audit records for external verification.

This modeling framework is essential for distinguishing, for each transition, what information becomes (or remains) externally observable—a precondition for local and global analysis of data leakage and attribution.

2. Differential Noninterference and Unwinding Techniques

Differential noninterference generalizes the notion of differential privacy to system executions: for any pair of executions that differ only in a single datum, the resulting distribution over observable traces diverges by at most a factor of $e^{\epsilon}$. The verification problem, then, is to show that this global property holds for potentially complex, interactive, and nonterminating systems.

To achieve this, the paradigm adapts unwinding proof techniques—originally used for classical noninterference (e.g., the Goguen–Meseguer unwinding theorem)—to the probabilistic and quantitative setting of differential privacy:

• A family of binary relations $\{R^{\epsilon}\}_{\epsilon \geq 0}$ is defined over system states, indexed by an “accumulated leakage” parameter $\epsilon$.
• For two states related by $R^{\epsilon}$, and for every observable action $a$, the conditional transition probability distributions are related via approximate lifting. Specifically, two distributions $\nu_1,\nu_2$ are related ($\nu_1 \mathrel{\mathcal{R}_{R,\delta}} \nu_2$) if there exists a bijection $\beta$ so that each paired state satisfies $R$ and for all $s$, $|\log \nu_1(s) - \log \nu_2(\beta(s))| \leq \delta$.
• This unwinding condition ensures that at every local step, the “distance” between future observable behaviors grows by no more than the privacy parameter.

By demonstrating that all reachable state transitions preserve this relation—often through inductive or algorithmic unwinding—the paradigm guarantees that the full system satisfies differential noninterference, thereby composably bounding per-datum attribution and leakage.

3. Mechanization through Automated Checking

The interactive verification paradigm supports efficient mechanical verification of candidate unwinding relations:

• The isUnwindFam algorithm iterates over all pairs of related states and actions in the I/O alphabet, computing “extended transitions” (including hidden steps) to produce probabilistic distributions over “H-disabled” states (states ready for observable actions).
• For each such pair, it constructs a bipartite graph and employs matching algorithms (e.g., Hopcroft–Karp) to determine if an approximate lifting with the correct $\delta$ exists. A perfect matching validates the pair for the given action.
• The isAllCovered algorithm checks that, for every reachable state and every data input, state transitions remain within the intended unwinding relation (i.e., the family $\{R^{\epsilon}\}$ “covers” all data inputs and system behaviors).

Polynomial-time mechanical checking of these conditions is tractable for finite-state systems, allowing deployment of this paradigm in practical settings, such as verifying privacy guarantees for systems inspired by PINQ.

4. Compositional Reasoning and Refinement

A defining feature is support for compositional verification:

• Subsystems, such as privacy-sanitation subroutines with known privacy guarantees (e.g., independently verified $\epsilon$-DP mechanisms), can be reasoned about in isolation.
• The system can be built using idealized transitions (atomic privacy actions), with global properties proved at this level. Subsequently, these transitions can be replaced (refined) by their full finite-state implementations, with the property that the overall observable trace behavior does not change (subroutine composition/refinement theorem).
• The linearity of the accumulated privacy loss is quantified: if a data point can influence up to $t$ queries, the total leakage is bounded by $2t\epsilon$ (the factor of 2 accounts for interactions affecting both query output and subsequent data handling).

By structuring verification in this way, local guarantees can be modularly combined, enabling scalable verification as systems evolve or are composed from independently verified modules.

5. Data Attribution and Privacy Leakage

Data attribution requires not only the ability to assign responsibility for data use, but also to bound the extent to which individual data points can influence observable outcomes. Within this framework:

• Every system transition (inputs, outputs, internal events such as scheduling) is mapped to a bounded increment in privacy leakage.
• The composition of these steps ensures that the aggregate leakage for any datum can be tracked and locally accounted for, yielding a traceable bound for audit or accountability.
• The resulting system trace provides modular, formal evidence that no more information is leaked about any individual than the privacy definition allows, regardless of system complexity, interactivity, or external auxiliary information.

Thus, the paradigm equips organizations with the means to audit, attribute, and defend data usage claims, particularly when external certification of privacy or accountability is needed, as in legal, medical, or governmental settings.

6. Technical Summary and Implications

The interactive verification paradigm for data attribution, as realized in the formal automaton and unwinding framework, provides:

• A precise and compositional semantics for interactive systems handling sensitive data.
• Unwinding relations for local-to-global quantitative analysis of privacy and data leakage.
• Mechanization via algorithmic checking (including formal reductions to perfect matching problems).
• Compositionality, supporting incremental, modular certification and refinement.
• Auditable attribution, allowing system traces to be certified as respecting formal privacy and data-use policies.

This approach ensures that privacy and attribution guarantees remain valid regardless of auxiliary information, future system refinements, or independent subsystem evolution. It enables practical, formal certification and accountability in complex data-driven systems. The resulting methods are broadly applicable wherever privacy-preserving, auditable data handling with robust semantic guarantees is required, and can be extended or adapted as new interactive data sharing paradigms and privacy models emerge.