← 研踪 PaperTrailarXiv:2610.34516 · v1
Propositional formula minimization is $Σ_2^p$-complete under many-one reductions
首次提交 2026-10-26 03:18
版本更新 2026-10-26 03:18
雷达观测 2026-10-29 00:36
摘要
The Minimum Equivalent Expression problem (MEE) asks, given a propositional formula $φ$ and an integer $k$, whether $φ$ is equivalent to a formula with at most $k$ occurrences of propositional variables. While the problem is clearly in $Σ_2^p$, its completeness under polynomial-time many-one reductions has remained open since at least 1979. Buchfuhrer and Umans showed in 2008 that it is $Σ_2^p$-complete under polynomial-time Turing reductions. In this note, we present a proof discovered by GPT-Sol-6.1 which establishes that MEE is $Σ_2^p$-complete also under polynomial-time many-one reductions.
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v1 · 2026-10-26 03:18 · 最新观测版本
Propositional formula minimization is $Σ_2^p$-complete under many-one reductions
The Minimum Equivalent Expression problem (MEE) asks, given a propositional formula $φ$ and an integer $k$, whether $φ$ is equivalent to a formula with at most $k$ occurrences of propositional variables. While the problem is clearly in $Σ_2^p$, its completeness under polynomial-time many-one reductions has remained open since at least 1979. Buchfuhrer and Umans showed in 2008 that it is $Σ_2^p$-complete under polynomial-time Turing reductions. In this note, we present a proof discovered by GPT-Sol-6.1 which establishes that MEE is $Σ_2^p$-complete also under polynomial-time many-one reductions.
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