DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

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.

The modified Post correspondence problem

Definition

An instance of the modified Post correspondence problem is a PCP instance $(u_{1}, v_{1}), \dots, (u_{n}, v_{n})$ with the extra requirement that a permitted match must start with the first domino.

Thus a modified-PCP match is a nonempty sequence $1 = i_{1}, i_{2}, \dots, i_{k}$ such that $u_{i_{1}} \dots u_{i_{k}} = v_{i_{1}} \dots v_{i_{k}} .$

Remarks

Modified PCP differs from ordinary PCP only by fixing the first chosen tile.
Every modified-PCP match is a PCP match, but not conversely.

Depends on

The Post correspondence problem

Used by

Dependency tree · one level

1 result within one dependency step 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

John Watrous, Introduction to the Theory of Computing (standard reference, not scraped)
MIT OpenCourseWare, Lecture 10: Computation History Method (standard reference, not scraped)