machine learning applications pumping lemma undecidability turing machines simplify grammar gnf cnf ambguity derivations pda cfg regular expressions conversion epsilon nfa minimization of dfa nfa dfa formal languages and automata theory multi layer remarks example: face recognition back propagation backpropagation gradient neural networks issues in decision tree learning information gain dis-advantages entropy decision tree concept learning internet of things issues perspectives well-posed learning problems flat unit 1
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