DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Exponential-mechanism utility sensitivity

Definition

Let $D$ be the finite-support count functions on a nonempty record universe, with add/remove-one-occurrence adjacency. Let $R$ be a nonempty finite set independent of the database, and let $u : D \times R \to R$ be a real-valued utility. When the set of adjacent-pair utility differences has an attained finite maximum, the global utility sensitivity of $u$ is

Δ_{u} = \max_{D \sim D^{'}, r \in R} ∣ u (D, r) - u (D^{'}, r) ∣ .

The sensitivity is positive when $Δ_{u} > 0$ ; the exponential mechanism on this page uses that positive-sensitivity case.

Definition references

The database domain and add/remove adjacency

Dwork and Roth, The Algorithmic Foundations of Differential Privacy, Definition 3.4, printed pp. 36–37.

Vadhan, The Complexity of Differential Privacy, Proposition 4.2, PDF pp. 33–34.

Depends on

Differential privacy, databases, and add/remove adjacency

Used by

Exponential mechanism Algorithm
Finite-range private selection Example
Exponential mechanism privacy and utility Theorem

Dependency tree · two levels

4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Cynthia Dwork and Aaron Roth, The Algorithmic Foundations of Differential Privacy (standard reference, not scraped)
Salil Vadhan, The Complexity of Differential Privacy, 2017 manuscript (standard reference, not scraped)