DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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.

Input encoding and size for algorithmic tasks

Definition

An input encoding is an injective map $enc$ from the declared instance set into ${0, 1}^{*}$ . The input size of an instance $z$ is $n : = ∣ enc (z) ∣$ . If task instances are already binary strings, the default encoding is the identity. The encoding is part of the task specification, and any length or padding convention must be stated.

For a task family, let $P_{n}$ denote the encoded instances of length $n$ that lie in its promise domain, with the decision sides or search relation inherited from QA task and promise domain. A statement indexed by input length $n$ concerns only $P_{n}$ .

Depends on

QA task and promise domain

Used by

All-zero versus exactly-one-marked search promise Definition
Amplitude estimation and counting input/output contract Definition
Binary dot product as parity Definition
Boolean oracle query model for search lower bounds Definition
Classical bit-operation cost Definition
Classical query algorithm Definition
Deutsch–Jozsa promise Definition
Finite marked-item search and its bit oracle Definition
Promise query instance and oracle family Definition
Promise-preserving reduction composes with a query solver Theorem

Dependency tree · two levels

2 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

Ronald de Wolf, Quantum Computing: Lecture Notes (standard reference, not scraped)
Andrew M. Childs, Lecture Notes on Quantum Algorithms (standard reference, not scraped)
John Preskill, Quantum Information, Chapter 6: Quantum Algorithms (standard reference, not scraped)