🤖 AI Summary
This work addresses the lack of a unified theoretical framework for k-prefix-, k-suffix-, and k-infix-free languages by proposing two general formalisms based on partial orders and finite-state transducers, thereby integrating these three classes of marginal code languages into a single coherent system for the first time. Building on this foundation, the study systematically generalizes the notion of marginal variants to any code-related language definable by transducers and investigates their uniform satisfiability and maximality properties. The research not only establishes a unified theoretical basis for marginal code languages but also advances the decidability analysis of their key properties, offering novel methodological tools for formal language theory and coding theory.
📝 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.
