Abstract: A method and apparatus are disclosed that compress an input string to an equivalent word relative to a noncommutation graph. The disclosed compression system compresses an input string in a manner that an equivalent string is produced upon decompression. The disclosed compression algorithms are based upon normal forms. First, a normal form of the interchange class is produced containing the source output string. Thereafter, a grammar-based lossless data compression scheme (or another compression scheme) is applied to the normal form. Upon decompression, the compressed string produces an equivalent string. A normal form generation process is employed to compute the lexicographic normal form or the Foata normal form of an interchange class from one of its members, using only a single pass over the data.

Abstract: A combinatorial approach is disclosed for analyzing a class of plurally parsable dictionaries for predictable, discrete, memoryless sources. A class of plurally parsable dictionaries are disclosed for a binary, memoryless source that outperforms the Tunstall code, when the probability of one of the symbols having a binary value of zero is sufficiently close to one. Given the probability of a symbol having a value equal to zero, p0, and the desired size of the dictionary, M, a dictionary is derived that provides. better compression than the Tunstall dictionary, if such a better dictionary exists. A Tunstall dictionary is initially selected having a size M—n, where n≧1. Thereafter, n all zero entries are added to the Tunstall dictionary. For the case where n equals one, the entry is comprised of a string of l zeroes. An equation is provided for obtaining the value of l. The improved dictionary is created by adding the all zero words (0l word for n=1) to the selected Tunstall dictionary.