More than a quarter of a century ago, the question of the complexity of determining whether a given Boolean formula is minimal motivated Meyer and Stockmeyer to define the polynomial hierarchy. This problem (in the standard formalized version---that of Garey and Johnson) has been known for decades to be coNP-hard and in NPNP, and yet no one had even been able to establish (many-one) NP-hardness. In this paper, we show that and more: The problem in fact is (many-one) hard for parallel access to NP.
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