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1
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0022092665
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(a) A more complete description of the abacus (with a figure) appears in a recent review by
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(1985)
Sci. Am.
, vol.253
, Issue.1
, pp. 48
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Bennett, C.H.1
Landauer, R.2
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2
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84927201350
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This paper contains an excellent discussion of the fundamental physical limits of computation.
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3
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84927201341
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See also R. Landauer, Found. Phys. (to be published). (b) A low noise temperature means that the coupling of phonons to the logical components is very weak, so that the thermalization of the latter may not occur until after a time considerably longer than the duration of the calculation. Unfortunately, modern-day computer elements do not satisfy the criterion;
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4
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0018960285
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: ``When transistors are increasingly miniaturized, the energy needed to drive the switching action becomes so small that it is comparable to the thermal energy of electrons in the device. When this happens, a well-defined switching behavior ceases to be obtainable.''
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(1980)
Science
, vol.208
, pp. 1246
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Robinson, A.L.1
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10
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84927201340
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A Turing machine consists of a read/write head having a finite number of internal states, and an infinite tape carrying symbols from a finite alphabet. The head reads one symbol on the tape, may replace it by another symbol according to prescribed rules, may likewise alter its internal state, and then the head moves one step (to the left or right) along the tape, or halts. It can be shown that a suitably programmed Turing machine can mimic any computer (albeit very inefficiently). For further details and references, see J. E. Hopcroft, Sci. Am. 250(5), 86 (1984).
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28
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84927201338
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There exist in modern-day technology asynchronous circuits (see Ref. 15, p. 114) which are usually very fast because they do not depend on the frequency of a clock (the latter is in most cases well below the speed of operation of a free-running gate). The orderly execution of operations in asynchronous circuits is controlled by completion and initiation signals, so that the completion of one operation initiates the execution of the next. However, in current computers, these asynchronous circuits are restricted to auxiliary tasks, such as communicating with peripheral equipment. What I have in mind here is a computer where the CPU itself is asynchronous.
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29
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84927201337
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Consider the identity sum xk=(1-xM) /(1-x), where the sum runs from 0 to M-1. By applying n times the operator x partial / partial x, one obtains an explicit expression for sum knxk. In particular, the sum (10) can be evaluated by taking x=e2 π i(r-s)/M , so that xM=1.
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31
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84927201336
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76, 749 (1949).
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32
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84927201335
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The computer which is described by this Hamiltonian is not a true Turing machine in the usual sense, since the latter must have an infinite tape. A Turing machine may reach the logical end of a computation after a finite number of steps, or may never halt. The number of steps is often unpredictable—this is the famous ``halting problem.'' Here on the contrary, the total number of steps, N, is prescribed once for all by the hardware. The nontrivial part of the computation may, of course, end in fewer steps, e.g., we may add two small integers while very long registers are available. In that case, the following Uk matrices act as unit matrices on the remaining logical states ψk (exactly as in an ordinary adder, based on modern-day technology). It is also possible that N steps are not enough to obtain the desired result. In that case, one may concatenate several subprograms, as explained at the end of Sec. IV.
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39
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In this paper, I shall not discuss whether such a computer can be manufactured now with modern-day technology or in the foreseeable future. In particular, I do not describe how the input is prepared and how the output is measured. I am solely concerned with problems of principle
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41
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0002735562
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Physical versus Logical Coupling in Memory Systems
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This ought to be called logical redundancy. There may also be physical redundancy, whereby several dichotomous elements are coupled together so as to make one larger object (for example, a magnetic domain) representing a single bit. The optimum mix of these two types of redundancy was discussed by
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(1960)
IBM Journal of Research and Development
, vol.4
, pp. 305
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Swanson, J.A.1
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43
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It is even recommended to do so, see Ref. 15, p. 255: ``In practice it is important that the error-correction mechanism will not just correct errors but will also provide a warning signal. . .''
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44
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84927201321
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In principle, one could use the same set of SG apparatuses successively for each triple of spins. However, one would then have to ``cool'' the apparatuses (to reset them to a pure state) before each use. Otherwise, if the SG apparatuses are left in a correlated state, they will only propagate errors from one triple to the next.
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46
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84927201320
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Each subprogram may have its own cursor, or the same cursor may be used for various subprograms.
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49
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84927201319
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Proceedings of the Tenth International Symposium on Multiple-Valued Logic, Evanston, Illinois, 1980 (IEEE Computer Society, Long Beach, California, 1980).
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