We present a uniform approach for solving language inclusion problems. Our approach relies on a least fixpoint characterization and a quasiorder to compare words of the "smaller" language, reducing the inclusion check to a finite number of membership queries in the "larger" language. We present our approach in detail on the case of inclusion of a context-free language given by a grammar into a regular language. We then explore other inclusion problems and discuss how to apply our approach.
翻译:我们提出了一种解决语言包含问题的统一方法。该方法基于最小不动点刻画和一种准序来比较“较小”语言的单词,将包含检查简化为对“较大”语言进行有限次成员查询。我们以通过文法给出的上下文无关语言包含于正则语言的情况为例,详细阐述了该方法。随后,我们探讨了其他包含问题,并讨论了如何应用我们的方法。