The 4^k Barrier for the k-Distinct Language
Can the $k$-distinct language - words over $[n]$ of length at most $k$ with no repeated symbol - be recognized by an acyclic NFA of size $c^k n^{O(1)}$ for some $c < 4$? A construction of size $2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)}$ answers yes.
Exact FrontierDelta
Scope and record
Occurred: Jul 28, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: The 4^k Barrier for the k-Distinct Language · k-distinct barrier
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
ChatGPT / Codex 5.4-5.6 Pro
model · ai model contributor · OpenAI / Google DeepMind
Gemini 3.1 Pro
model · ai model contributor · OpenAI / Google DeepMind
Lineage and corrections
This event attributed to Gemini 3.1 Pro
This event attributed to ChatGPT / Codex 5.4-5.6 Pro