一句话：从逻辑可定义性角度研究伪随机有限结构，并分类哪些逻辑转换可作为伪随机生成器。
论文研究逻辑可定义性视角下的伪随机性与伪随机生成器。作者结合经典去随机化与有限模型论结果，证明可在多项式时间内确定性地构造图和关系结构，使其与随机结构对任意一阶逻辑或最小不动点逻辑句子统计不可区分。由此提出核心问题：这种构造能否由熵更低的简单结构经逻辑转换实现，即逻辑公式能否充当伪随机生成器。论文针对一阶逻辑、不动点逻辑以及带奇偶量词的不动点逻辑，完整刻画了何时可能；对带奇偶量词的一阶逻辑给出部分结果与猜想。
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in polynomial time, graphs and relational structures that are statistically indistinguishable from random structures by any sentence of first order or least fixed point logics. This raises the question of whether such constructions can be implemented via logical transductions from simpler structures with less entropy. In other words, can logical formulas be pseudorandom generators? We provide a complete classification of when this is possible for first order logic, fixed point logic, and fixed point logic with parity, and provide partial results and conjectures for first order logic with parity.