Finite State Models in the Study of Comma-Free Codes

The definition of comma-free codes is extended to be more comprehensive and include codes with variable length codewords and codes with an unlimited number of codewords. Finite state recognizers are used to represent commafree codes in a compact form, making available the well established methods of manipulating and analysing finite state models. An efficient algorithm is presented to test the comma-freeness of any given code represented by a finite state recognizer. It is well known, that any maximal comma-free code with codewords of odd fixed length can be achieved. Although upper limits have been given for even fixed length it has not been established which comma-free codes of this nature can achieve the upper limit. Compact representations of comma-free binary codes are given for variable length codewords with maximum even fixed lengths (6,8 and 10) and in one case (length not greater than 6) it is seen that the corresponding upper limit for fixed lengths can be exceeded.