We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for writing programs that evaluate expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tree automata, which allows us to derive new decidable learning results and decision procedures for several expression learning problems by writing programs in the programming language.

翻译：我们研究了带有语法约束的表达式学习问题，并引入了有限维度可检查语言这一概念，用以刻画具有可判定学习性的符号语言。这类语言的语义可通过有限数量的辅助信息来定义，该信息独立于表达式规模，但依赖于固定的评估结构。我们提出了一种通用编程语言，用于编写评估表达式语法树的程序，并给出一个元定理，将该类语言对应的程序与有限树自动机建立关联。通过在该编程语言中编写程序，我们得以推导出若干表达式学习问题中新的可判定学习性结果与判定过程。