structure of the target phenomenon, for various reasons researchers in this approach standardly provide a concrete model: an actual computer programmed so that (hopefully) it realizes the same (or a relevantly similar) abstract computational system as is realized by the cognitive systems under study. If the concrete model appears able to perform actual cognitive tasks in much the way people do,...

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The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomial-time does this imply the polynomial-time hierarchy collapses? We give a relativized negative answer to this question by exhibiting an oracle...