Complete VariableLength Codes: An Excursion into Word Edit Operations Given an alphabet A and a binary relation xcfx84 xe2x8ax86 A * xc3x97 A * , a language X xe2x8ax86 A * is xcfx84independent if xcfx84 (X) xe2x88xa9 X  xe2x88x85; X is xcfx84closed if xcfx84 (X) xe2x8ax86 X. The language X is complete if any word over A is a factor of some concatenation of words in X. Given a family of languages F containing X, X is maximal in F if no other set of F can stricly contain X. A language X xe2x8ax86 A * is a variablelength code if any equation among the words of X is necessarily trivial. The study discusses the relationship between maximality and completeness in the case of xcfx84independent or xcfx84closed variablelength codes. We focus to the binary relations by which the images of words are computed by deleting, inserting, or substituting some characters.

Restrictions and Generalizations on CommaFree Codes A significant sector of coding theory is that of commafree coding; that is, codes which can be received without the need of a letter used for word separation.  The major difficulty is in finding bounds on the maximum number of commafree words which can inhabit a dictionary.  We introduce a new class called a selfreflective commafree dictionary and prove a series of bounds on the size of such a dictionary based upon word length and alphabet size.  We also introduce other new classes such as selfswappable commafree codes and commafree codes in  q  dimensions and prove preliminary bounds for these classes. Finally, we discuss the implications and applications of combining these original concepts, including their implications for the NPcomplete Post Correspondence Problem.