关于语言族强替换性的一个命题

One Proposition for the Strong Replaceability of Families of Languages

一个语言族能被有限分支自动机识别等价于它是自相容的且是有限可微的,而自相容的语言族又等价于它是闭的且具有替换性。自从语言族的微商运算的逆运算积分被引入到语言族的研究中以后,语言族的替换性利用语言族的积分被推广到强替换性,从而自相容性、可识别性分别被推广到强自相容性和强可识别性。同时,自相容性与可微性这两个原本独立的概念之间产生了某种联系。这种联系体现在用积分给出了语言族具有替换性的一个充分必要条件上,后来,这个充分必要条件又被推广到强替换性上。讨论了关于语言族具有强替换性的这个充分必要条件,指出其必要性不成立并给出了一个新的必要条件。本文同时给出了充分条件的一个新的证明。

After the author introduces the integration of families of languages Xdu, which is the inverse operation of the differential coefficient of families of languages, the replaceablity of families of languages may be generalized to the strong replaceablity. The self-compatibility of families of languages may be generalized to the strong self-compatibility, and finally, we may generalize the recognizable concept of families of languages to their strong recognizable concept. Lei generalized the sufficient and necessary conditions under which families of languages have replaceability, and he introduced a sufficient and necessary condition under which families of languages have strong replaceability. This paper points out that the necessity of this sufficient and necessary condition can not be established, and has corrected it. Meantime, the paper introduces a new proof of sufficiency.