Recognizing sources of random strings

The identification of a source given a sequence of random strings is discussed. Two modes of random string generation are analyzed. In the first mode, arbitrary strings are generated in which the individual symbols occur exactly once in each random string. The latter case corresponds to the situation in which the sources generate random permutations. In both cases, the best match to the distribution being used by each source can be obtained by maintaining an exponential number of statistics. This being infeasible, a simple parameterization of the distributions is proposed. For arbitrary strings, the simple unigram-based model (U-model) is proposed. For the case of permutations, a new model called the S-model is proposed, and it is used to analyze and/or approximate unknown distributions of permutations. The relevant estimation procedures, together with the applications to source recognition, are presented. The method presents a unique blend of syntactic and statistical pattern recognition