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Inasmuch as security is dependent on most recent scientific and technological innovations, some of the relevant fundamental challenges are: detecting, recognizing, interpreting, and ultimately assigning meaning to strings of symbolic information, whether it is biological data, biometric data, intelligence information, or any other form of information. The research reviewed in this paper addresses the above problem from a mathematical/information-theoretic point of view, proposing a number of methods for fast exact and non-exact string matching, pattern recognition, and grammar detection. The proposed methods are: the Stern-Brocot Transform, the Cyclic Transform, the Unbalanced Haar Transform and the Haar-Riesz Product.
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