AI 中文总结
本文通过结合迭代双赢范式、范围回避问题还原和PCP定理，证明了指数时间与Merlin-Arthur查询的复杂性类的近最大电路下界。
AI 中文摘要
我们证明了复杂度类\(\mathsf{E}^{\mathrm{pr}\mathsf{MA}}/_1\)的近最大（\(2^n / n\)）电路下界，该类对应于可访问承诺\(\mathsf{MA}\)预言机和一位建议的指数时间。我们的证明融合了迭代双赢范式、从范围回避问题到电路下界的归约以及PCP定理。证明的关键是对复杂度类\(\mathsf{P}^\mathsf{NP}[{\textsf{#rounds}}=r, {\textsf{length}}=s]\)的分析，它是具有\(r(n)\)轮自适应\(\mathsf{NP}\)查询的\(\mathsf{P}^\mathsf{NP}\)，每个\(\mathsf{NP}\)查询有见证长度\(s(n)\)。
英文摘要
We prove a near-maximum ($2^n / n$) circuit lower bound for the complexity class $\mathsf{E}^{\mathrm{pr}\mathsf{MA}}/_1$, corresponding to exponential time with access to a promise-$\mathsf{MA}$ oracle and one bit of advice. Our proof incorporates the iterative win-win paradigm (Chen--Lu--Oliveira--Ren--Santhanam, FOCS'23), the reduction from the Range Avoidance problem to circuit lower bounds (Jeřábek, Ann. Pure Appl. Log. '04; Korten, FOCS'21), and the PCP theorem. Crucial to our proof is the analysis of the complexity class $\mathsf{P}^\mathsf{NP}[{\textsf{#rounds}}=r, {\textsf{length}}=s]$, which is $\mathsf{P}^\mathsf{NP}$ with $r(n)$ adaptive rounds of $\mathsf{NP}$ queries, where each $\mathsf{NP}$ query has witness length $s(n)$.
