AI 中文总结
该研究针对显式仿射见证隔离，通过随机变换的成功保证推导NP⊆P/poly等复杂度坍缩结论，明确了仿射分量数量与成功保证的关联条件。
AI 中文摘要
我们研究随机非均匀多项式规模变换，该变换针对非空满足集为仿射的电路输入输出显式二元仿射滤波器，滤波器可依赖整个输入描述，无需提供仿射基。对每个固定的δ<1，最坏情况单元素成功保证Ω(n^(-δ))（n为见证元数）意味着NP⊆P/poly。更一般地，任何成功保证ω(log n/n)，对长度为s、含至多v个见证变量的描述，可得到规模为(s+2)^(O(1))2^(o(v))的可满足性电路，当s=v^(O(1))时对v呈亚指数级。反之，SAT搜索到决策给出确定性完美隔离，使多项式资源固定指数强仿射隔离等价于NP⊆P/poly。对至多n^β个仿射分量的显式并集，当β,δ≥0且β+δ<1时，成功Ω(n^(-δ))意味着相同坍缩，未声明逆线性端点。
英文摘要
We study randomized nonuniform polynomial-size transformations that output explicit binary affine filters for circuit inputs whose nonempty satisfying sets are affine. The filter may depend on the entire input description; no affine basis is supplied. For every fixed $δ<1$, a worst-case singleton success guarantee $Ω(n^{-δ})$, where $n$ is the witness arity, implies $NP\subseteq P/poly$. More generally, any success guarantee $ω(\log n/n)$ yields satisfiability circuits of size $(s+2)^{O(1)}2^{o(v)}$ for length-$s$ descriptions with at most $v$ witness variables, hence subexponential in $v$ when $s=v^{O(1)}$. Conversely, SAT search-to-decision gives deterministic perfect isolation, making polynomial-resource fixed-exponent strong affine isolation equivalent to $NP\subseteq P/poly$. For explicit unions of at most $n^β$ affine components, success $Ω(n^{-δ})$ implies the same collapse whenever $β,δ\ge0$ and $β+δ<1$. The inverse-linear endpoint is not claimed.
