OpenFrontiers
Join
← Back to the index
OP-6571OpenAlgorithms and data structures

Reset threshold of the cyclic pair-compression automaton

TheoremDB P2560 · automata theory

MSC 68W · Algorithms in computer science

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

For n≥3n\ge 3, define a binary automaton AnA_n on states {0,…,n−1}\{0,\ldots,n-1\} by a(i)=i+1(modn)a(i)=i+1\pmod n, while b(i)=ib(i)=i for even ii and b(i)=i−1b(i)=i-1 for odd ii. Is AnA_n synchronizing exactly when nn is odd, with reset threshold n(n−1)/2n(n-1)/2 in every odd case?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

References
  1. [1]TheoremDB P2560 link

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.