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.

Complexity of SuffixFree Regular Languages A sequence ((L_k,L_k1 dots )) of regular languages in some class (mathcal C), where n is the state complexity of (L_n), is called a stream. A stream is most complex in class (mathcal C) if its languages together with their dialects (that is, languages that differ only very slightly from the languages in the stream) meet the state complexity bounds for boolean operations, product (concatenation), star, and reversal, have the largest syntactic semigroups, and have the maximal numbers of atoms, each of which has maximal state complexity. It is known that there exist such most complex streams in the class of regular languages, and also in the classes of right, left, and twosided ideals. In contrast to this, we prove that there does not exist a most complex stream in the class of suffixfree regular languages. However, we do exhibit one ternary suffixfree stream that meets the bound for product and whose restrictions to binary alphabets meet the bounds for star and boolean operations. We also exhibit a quinary stream that meets the bounds for boolean operations, reversal, size of syntactic semigroup, and atom complexities. Moreover, we solve an open problem about the bound for the product of two languages of state complexities m and n in the binary case by showing that it can be met for infinitely many m and n.