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We consider the efficient generation of solved instances of computational problems. In particular, we consider invulnerable generators. Let S be a subset of {0,1}* and M be a Turing Machine that accepts S; an accepting computation w of M on input x is called a "witness" that x 驴 S. Informally, a program is an 驴-invulnerable generator if, on input 1n, it produces instance-witness pairs (x, w), with |x| = n, according to a distribution under which any polynomial-time adversary who is given x fails to find a witness that x 驴 S, with probability at least 驴, for infinitely many lengths n.The question of which sets have invulnerable generators is intrinsically appealing theoretically, and the results can be applied to the generation of test data for heuristic algorithms and to the theory of zero-knowledge proof systems. The existence of invulnerable generators. is closely related to the existence of cryptographically secure one-way functions. We prove three theorems about invulnerability. The first addresses the question of which sets in NP have invulnerable generators, if indeed any NP sets do. The second addresses the question of how invulnerable these generators are.