Some Remarks on Marginal Code Languages

Abstract

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.