Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 129-02. An exponential two-way deterministic state lower bound for one-way liveness
Manuscript map · lines 4915–4924
OpenAI@2026-10-07#rem:oai-p-129-02
Authors: OpenAI. Family 129.
Title: An exponential two-way deterministic state lower bound for one-way liveness.
Abstract: One-way liveness on h points accepts a word of binary relations when their ordered product is nonempty. For every h ≥ 2, it has a nondeterministic automaton with $h+3$ states and no left moves, whereas every equivalent s-state two-way deterministic automaton satisfies $4(s+2){}2{}ge2{}{{}lfloor(h-2)/31{}rfloor}$. Partial transition rules, stay moves, and nonaccepting infinite computations are allowed. The alphabets are finite and grow with h, so the result rules out an alphabet-independent polynomial state bound for deterministic two-way simulation, already for one-way nondeterministic sources.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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