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This paper presents the comparison between algorithms used to find inexact motifs (transformed into a set of exact sub-sequences) in a DNA sequence. The MFA algorithm builds an automaton that searches for the set of exact sub-sequences by building a finite automaton in a similar way to the KMP algorithm. This algorithm is compared against the traditional automaton using the basic idea of the subset construction. This traditional algorithm is implemented using some characteristics to increase its performance which will end in an algorithm that can be proven to have the optimal number of states.