Generalizations of Code Languages with Marginal Errors

The k-prefix-free, k-suffix-free and k-infix-free languages generalize the prefix-free, suffix-free and infix-free languages by allowing marginal errors. For example, a string x in a k-prefix-free language L can be a prefix of up to k different strings in L. We also define finitely prefix-free languages in which a string x can be a prefix of finitely many strings. We present efficient algorithms that determine whether or not a given regular language is k-prefix-free, k-suffix-free or k-infix-free, and analyze the time complexity of the algorithms. We establish undecidability results for deciding these properties for (linear) context-free languages.