This paper addresses the problem of improving the accuracy of hypotheses output by a learning algorithm in the distribution-free (PAC) learning model. The paper introduces the concepts of strong learnability and weak learnability, where a concept class is strongly learnable if there exists a polynomial-time algorithm that achieves low error with high confidence, and is weakly learnable if the learner can produce an hypothesis that performs slightly better than random guessing. The main result of the paper is a proof that strong and weak learnability are equivalent. This equivalence is demonstrated through a method for converting a weak learning algorithm into one that achieves arbitrarily high accuracy. The construction uses filtering to modify the distribution of examples, forcing the weak learning algorithm to focus on harder-to-learn parts of the distribution. The paper also discusses the theoretical and practical implications of this equivalence, including bounds on the complexity of strong learning algorithms and the efficiency of converting weak learning algorithms into strong ones. Additionally, the paper provides a detailed analysis of the running time and space complexity of the resulting strong learning algorithm, showing that it runs in polynomial time and has relatively modest space requirements. Finally, the paper describes a modification to the construction that significantly improves the time and sample complexity, achieving bounds that are linear in \(1/\epsilon\).This paper addresses the problem of improving the accuracy of hypotheses output by a learning algorithm in the distribution-free (PAC) learning model. The paper introduces the concepts of strong learnability and weak learnability, where a concept class is strongly learnable if there exists a polynomial-time algorithm that achieves low error with high confidence, and is weakly learnable if the learner can produce an hypothesis that performs slightly better than random guessing. The main result of the paper is a proof that strong and weak learnability are equivalent. This equivalence is demonstrated through a method for converting a weak learning algorithm into one that achieves arbitrarily high accuracy. The construction uses filtering to modify the distribution of examples, forcing the weak learning algorithm to focus on harder-to-learn parts of the distribution. The paper also discusses the theoretical and practical implications of this equivalence, including bounds on the complexity of strong learning algorithms and the efficiency of converting weak learning algorithms into strong ones. Additionally, the paper provides a detailed analysis of the running time and space complexity of the resulting strong learning algorithm, showing that it runs in polynomial time and has relatively modest space requirements. Finally, the paper describes a modification to the construction that significantly improves the time and sample complexity, achieving bounds that are linear in \(1/\epsilon\).