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*To*: [email protected]*Subject*: Crypto and new computing strategies*From*: [email protected] (Eric Hughes)*Date*: Wed, 30 Mar 94 12:09:09 -0800*In-Reply-To*: Jim choate's message of Wed, 30 Mar 1994 11:54:07 -0600 (CST) <[email protected]>*Sender*: [email protected]

>I am not shure that it has been demonstrated that a QM mechanis is necessarily >solely of a Turing architecture. The Bekenstein Bound gives limits both on the expected maximum number of quantum states encodable in a given volume of space and on the expected maximum number os transitions between these states. If this bound holds (and it certainly seems to hold for EM fields), then a probabilistic Turing machine will be able to simulate it. >Also there is the potential to use neural networks at these levels (which are >not necessarily reducable to Turing models, the premise has never been proven) If you have infinite precision, the statement is unproven. If you have finite precision, you get a Turing machine. You never get infinite precision in real life, even with quantum superposition. Steve Smale did some work a few years ago where he made Turing-type machines out of real numbers, i.e. infinite precision. P=NP for this model, and the proof is fairly easy. From an information-theoretic point of view, you can encode two real numbers inside of another one and do computations in that encoded form, because a real number encodes an infinite amount of information. If it's finite, it's a Turing machine. If it's expected finite, it's a probabilistic Turing machine. If it's infinite, it cannot be implemented in hardware. Eric

**Follow-Ups**:**Re: Crypto and new computing strategies***From:*Jim choate <[email protected]>

**References**:**Re: Crypto and new computing strategies***From:*Jim choate <[email protected]>

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