Alphabeta MathHow 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.
FALSE: PCP permits reordering symbols inside a domino
Statement
In a PCP match, one may reorder the symbols inside a chosen domino before concatenating it.
Facts & Assumptions
Given: The one-domino PCP instance
A PCP match must satisfy equality of the literal top and bottom concatenations of the chosen domino sequence, by The Post correspondence problem.
Refutation
If one were allowed to reorder symbols inside the domino, the unique tile could be changed from to by swapping the bottom symbols, and then a one-tile sequence would look like a match.
In actual PCP, [L1] forbids that operation. The only nonempty sequences use the same domino some number of times, yielding top word and bottom word . Their first symbols are always different, so these words are never equal.
Therefore the claimed permission is false: PCP concatenates whole dominoes in the chosen order and does not allow symbol reordering within a tile.
Depends on
Used by
Dependency tree · one level
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Sources
- John Watrous, Introduction to the Theory of Computing (standard reference, not scraped)