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The chapter defines the notion of a generator and its hardness, and formulates the hardness conjecture. It also defines a stronger notion of pseudosurjectivity of a generator and states the key conjecture about it. It examines some consequences of the two conjectures for the dWPHP problem. It also relates the hardness conjecture to feasible interpolation, gives a model-theoretic view of the issues and discusses a relation to pseudorandomness.
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