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We consider the problem of recognizing a vocabulary--a collection of words(sequences) over a finite alphabet--from a potential subsequence of one of itswords. We assume the given subsequence is received through a deletion channelas a result of transmission of a random word from one of the two genericunderlying vocabularies. An exact maximum a posterior (MAP) solution for thisproblem counts the number of ways a given subsequence can be derived fromparticular subsets of candidate vocabularies, requiring exponential time orspace.  We present a polynomial approximation algorithm for this problem. Thealgorithm makes no prior assumption about the rules and patterns governing thestructure of vocabularies. Instead, through off-line processing ofvocabularies, it extracts data regarding regularity patterns in thesubsequences of each vocabulary. In the recognition phase, the algorithm justuses this data, called subsequence-histogram, to decide in favor of one of thevocabularies. We provide examples to demonstrate the performance of thealgorithm and show that it can achieve the same performance as MAP in somesituations.  Potential applications include bioinformatics, storage systems, and searchengines.

A Subsequence-Histogram Method for Generic Vocabulary Recognition over Deletion Channels