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Learning indexed families of recursive languages from positive data: A survey

机译：从积极数据中学习索引的递归语言族：一项调查

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摘要

In the past 40 years, research on inductive inference has developed along different lines, e.g., in the formalizations used, and in the classes of target concepts considered. One common root of many of these formalizations is Gold's model of identification in the limit. This model has been studied for learning recursive functions, recursively enumerable languages, and recursive languages, reflecting different aspects of machine learning, artificial intelligence, complexity theory, and recursion theory. One line of research focuses on indexed families of recursive languages - classes of recursive languages described in a representation scheme for which the question of membership for any string in any of the given languages is effectively decidable with a uniform procedure. Such language classes are of interest because of their naturalness. The survey at hand picks out important studies on learning indexed families (including basic as well as recent research), summarizes and illustrates the corresponding results, and points out links to related fields such as grammatical inference, machine learning, and artificial intelligence in general. (C) 2008 Elsevier B.V. All rights reserved.
机译：在过去的40年中，归纳推理的研究沿着不同的方向发展，例如在所使用的形式化以及所考虑的目标概念类别中。这些形式化的许多共同根源是Gold的极限识别模型。已经对该模型进行了研究，以学习递归函数，递归可枚举语言和递归语言，从而反映了机器学习，人工智能，复杂性理论和递归理论的不同方面。一项研究集中在递归语言的索引族上-表示方案中描述的递归语言类别，对于该递归语言，可以使用统一的程序有效地确定任何给定语言中的任何字符串的成员资格问题。由于其自然性，此类语言类很受关注。手头的调查挑选了关于学习索引家庭的重要研究（包括基础研究和最新研究），总结并说明了相应的结果，并指出了与相关领域（如语法推断，机器学习和人工智能）的链接。 （C）2008 Elsevier B.V.保留所有权利。

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