Some Remarks on Marginal Code Languages

TL;DR

This paper introduces a unified framework for marginal code languages, extending prefix, suffix, and infix-free languages by allowing limited prefix overlaps, and explores their properties using partial orders and transducers.

Contribution

It unifies the definitions of k-prefix-free, k-suffix-free, and k-infix-free languages through two methods, enabling the study of marginal versions of known code classes.

Findings

Unified definitions via partial orders and transducers.

Extended the class of code languages with marginal variants.

Analyzed satisfaction and maximality problems for these classes.

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.