Theoretical computer science · Jul 22, 2026
Černý bound for positive-level one-cluster automata
For the specified one-cluster automata with cycle length m and positive level ℓ, a reset-word bound (m-1)(n-1)+mℓ≤(n-1)² is reported.
Scope and what remains
A special-family result, not a resolution for all synchronizing automata; retain the positive-level hypothesis.
Contributors
Yinfeng Zhu, using OpenAI Codex / GPT-5.6 Sol Ultra.
AI systems: Codex, GPT-5.6 Sol Ultra