Studies on Efficient Learning Algorithms from Examples

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We have established a polynomial-time algorithm for exactly learning simple deterministic languages via membership queries, given a representative sample of the target language. This algorithm sophisticatedly employs a polynomial-time algorithm for checking the equivalence of simple deterministic languages that was devised by ourselves previously.For a real-time deterministic restricted one counter automation (droca) which has exactly one transition rule per one terminal symbol, a polynomial-sized characteristic sample is exactly obtained. Based on this result, we have devised an algorithm for identifying droca's in the limit with polynomial updating time and polynomial number of updates.We have developed an algorithm for approximately learn certain Boolean functions, called AC^0, from examples of their behavior with possibly attribute and classification noise, provided we are given the upper bound of the noise ratio which is less than 1/2. Subsequently, we devised an algorithm for guessing the upper bound of the noise ratio. Combining these results, we have succeeded in designing and algorithm for approximately learn such functions without any knowledge of the noise ratio in advance.Some algorithms were devised to identify some subregular languages in the limit from positive samples. Then we gave a unified method to identify some classes of languages in the limit from positive examples.Algorithms for finding a maximum clique in a graph are important for clustering problems. Then we devised a very fast algorithm for finding a maximum clique together with some extensions. We have successfully applied these algorithms for some practical problems as in bioinformatics, image processing, and so on.