Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 138-02. A Low-Space Algorithm for Worst-Case Subset Sum
Manuscript map · lines 5075–5084
OpenAI@2026-10-07#rem:oai-p-138-02
Authors: OpenAI. Family 138.
Title: A Low-Space Algorithm for Worst-Case Subset Sum.
Abstract: We give a uniform classical randomized decision algorithm for worst-case Subset Sum. Under every fixed polynomial bound on input-integer bit length, it uses ${}mathop{{}mathrm{poly}}{}nolimits (n)2{}{n/2}$ time and ordinary $O(2{}{n/5})$ writable words of $O(n+b)$ bits, where b is the largest input bit length. Both resource bounds hold on every execution. The error is one-sided: the algorithm always rejects unsolvable instances and accepts each solvable instance with probability at least 2/3.
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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