在字符串上学习MSO可定义的假设
Learning MSO-definable hypotheses on string
摘要：
本文研究了一元二阶逻辑MSO公式所指定的假设条件下字符串数据的分类问题。目标是设计学习算法，使其在训练集大小的时间多项式中运行，与整个数据集的大小无关或至少是次线性的。我们证明了消极和积极的结果。如果数据集是一个未处理的字符串，我们的算法有本地访问，那么学习在次线性时间是不可能的，即使是在一个小片段的一阶逻辑定义的假设。如果我们允许对字符串数据进行线性时间预处理以构建索引数据结构，则MSO可定义的假设的学习可以在训练集的大小的时间多项式中进行，而与整个数据集的大小无关。
英文摘要：
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set, independently of or at least sublinear in the size of the whole data set. We prove negative as well as positive results. If the data set is an unprocessed string to which our algorithms have local access, then learning in sublinear time is impossible even for hypotheses definable in a small fragment of first-order logic. If we allow for a linear time pre-processing of the string data to build an index data structure, then learning of MSO-definable hypotheses is possible in time polynomial in the size of the training set, independently of the size of the whole data set.
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。
