DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Logspace many-one reduction

Definition

For languages $A, B \subseteq Σ^{*}$ , write $A \leq_{\log} B$ if a deterministic read-only-input logspace transducer computes a total function $f$ with $x \in A ⟺ f (x) \in B .$ The transducer writes $f (x)$ once on a write-only output stream. Equivalently, it may recompute a requested output position $f (x)_{j}$ in logarithmic work space. Since the internal configuration has only polynomially many states and the output stream is not readable, every halting such transducer has polynomial output length: otherwise a repeated internal configuration would repeat forever.

Depends on

A read-only-input logarithmic-space machine

Used by

P-completeness under logspace reductions Definition
Composing two logspace reductions through a virtual tape Example
Logspace reductions compose Lemma
Directed s-t connectivity is NL-complete 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

Arora and Barak, Computational Complexity, Definition 3.14 (standard reference, not scraped)