What was already known
The Sakoda–Sipser question asks the state cost of removing nondeterminism in two-way automata. The cited unrestricted deterministic lower bound for the growing-alphabet liveness family was quadratic.
AI involvement
OpenAI credits its internal model with the manuscript and proof artifacts; item-specific autonomy is not documented.
OpenAI is the credited author and the release says its internal model produced the mathematical manuscripts; item-specific independence is undocumented.
Importance
Rules out an alphabet-independent polynomial simulation bound for this one-way family.
Limitations
The result concerns growing alphabets and does not settle fixed-alphabet variants. The source-reported Lean proof was not independently rebuilt.
Technical verification
The released scope note states the liveness lower bound and links a matching Lean Comparator target. The formalization concerns growing alphabets and both acceptance conventions, with one sharper factor. The source reports a machine formalization.
Formal checking
Exponential two-way deterministic state lower bound for the h+3-state one-way liveness family over growing alphabets. Formal proof with scope note and OneWayLiveness Comparator statement
- Checker
- Lean 4 formal development in the OpenAI math release
- Scope
- Exponential two-way deterministic state lower bound for the h+3-state one-way liveness family over growing alphabets
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central lower-bound mechanism was found in the released release; Few is the evidence default.
Correction and publication history
Claims an exponential state lower bound in the growing-alphabet liveness family.
Read this published revision