A prefix code L satisfies the condition that no word of L is a proper prefix of another word of L. Recently, Ko, Han and Salomaa relaxed this condition by allowing a word of L to be a proper prefix of at most k words of L, for some `margin' k, introducing thus the class of k-prefix-free languages, as well as the similar classes of k-suffix-free and k-infix-free languages. Here we unify the definitions of these three classes of languages into one uniform definition in two ways: via the method of partial orders and via the method of transducers. Thus, for any known class of code-related languages definable via the transducer method, one gets a marginal version of that class. Building on the techniques of Ko, Han and Salomaa, we discuss the \emph{uniform} satisfaction and maximality problems for marginal classes of languages.
翻译:前缀码L满足条件:L中任意词都不是另一个词的严格前缀。最近,Ko、Han和Salomaa放宽了这一条件,允许L中的词至多是L中k个词的严格前缀(其中k为某个"边际"值),从而引入了k-前缀无关语言类,以及类似的k-后缀无关和k-中缀无关语言类。本文通过两种方式——偏序方法和转换器方法——将这三类语言的定义统一为一种规范定义。由此,对于任何可通过转换器方法定义的已知码相关语言类,均可得到其边际版本。基于Ko、Han和Salomaa的技术,我们讨论了边际语言类的\emph{统一}满足性问题与极大性问题。