并行博弈节省量词
Parallel Play Saves Quantifiers
AI总结：
针对线性序和字符串上的一阶量词复杂度，论文提出多结构博弈中的“并行博弈”技术，给出不同大小子集刻画所需量词数的近紧上界。
摘要：
表达一阶性质所需的量词数量，可由称为多结构（MS）博弈的双人组合博弈刻画。我们在线性序与字符串上进行这些博弈，并引入一种称为“并行博弈”的技术，在许多情况下可显著减少所需量词数量。线性序和字符串是有序结构最基本的代表，而这类结构历来极难分析。尽管如此，本文给出了刻画这些结构中不同大小子集所需量词数的上界，并证明这些上界在常数因子意义下是紧的；在某些情况下，对任意小的 ε，紧性甚至可达到 1+ε 因子。
英文摘要：
The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call "parallel play", that dramatically reduces the number of quantifiers needed in many cases. Linear orders and strings are the most basic representatives of ordered structures -- a class of structures that has historically been notoriously difficult to analyze. Yet, in this paper, we provide upper bounds on the number of quantifiers needed to characterize different-sized subsets of these structures, and prove that they are tight up to constant factors, including, in some cases, up to a factor of $1+\varepsilon$, for arbitrarily small $\varepsilon$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
