It is clear that these values are in the order shown

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Unformatted text preview: n certain circuit-layout constraints (cf. P8, Section 2). Essentially, with polynomial packing (corresponding to the Abelian-group connectivity of Euclidean space) 6.2. The InteractionNote that the second gatefrom the bottom should be pq . defined by Figure To↵oli, 1982) Gate. The interaction pq is the conservative-logic primitive some wires may have to be made longer than with exponential packing (corresponding to an abstract space 13a, which also assigns its graphical representation.7 with free-group connectivity) (Toffoli, 1977). In the billiard ball model, the interaction gate is realized simply as the potential locus of collision of two balls. With reference to Figure 14, let p, q be the values at a certain instant of the binary variables associated with the two points P, Q, and consider the values-four time steps later in this particular example-of the variables associated with the four points A, B, C, D. It is clear that these values are, in the order shown in the figure, pq, ¬pq, p¬q; and pq. In other words, there will be a ball at A if and only if there was a ball at P and one at Q; similarly, there will be a ball at B if and only if there was a ball at Q and none at P; etc. 6.3. Interconnection; Timing and Crossover; The Mirror. Owing to its AND and NOT capabilities, the interaction gate is clearly a universal logic primitive (as explained in Section 5, we assume the availability of input constants). To verify that these capabilities are retained in the billiard ball model, one FiguremakeThe mirrorone can realize solid dash) can be used to deflect a ball’s path (a), introduce a must 15. sure that (indicated by a the appropriate interconnections, i.e., that one can suitably route Figure II.24: “The mirror (indicated (c), and realize nontrivial crossover deflect sideways shift (b), introduce delay by a solid dash) can be used to we balls from one collision locus to another andamaintain proper timing. In particular, since(d). are considering a ball’smust provide a way of performin...
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This document was uploaded on 03/14/2014 for the course COSC 494/594 at University of Tennessee.

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