What was already known
Vardi gave an exponential one-way construction for complementation, while lower bounds were known for sweeping automata. The unrestricted two-way complement question remained open in the manuscript’s account.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Rules out a polynomial complementation state bound uniform over finite alphabets.
Limitations
The construction uses an alphabet that grows with n and does not prove the same lower bound over one fixed alphabet.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every n≥4, an explicit n-state two-way nondeterministic finite automaton has a complement requiring at least ½·2^⌊(n−4)/127⌋−1 states in any two-way nondeterministic finite automaton.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision