A Lower Bound on Computational Complexity Given by Revelation Mechanisms
This paper establishes a lower bound on the computational complexity of smooth functions between smooth manifolds. It generalizes one for finite (Boolean) functions obtained (by Arbib and Spira ) by counting variables. Instead of a counting procedure, which cannot be used in the infinite case, the dimension of the message space of a certain type of revelation mechanism proves the bound. It also provides an intrinsic measure of the number of variables on which the function depends. This measure also gives a lower bound on computational costs associated with realizing or implementing the function by a decentralized mechanism, or by a game form.
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Volume (Year): 7 (1996)
Issue (Month): 2 (February)
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