Unformatted text preview: vents, represented by conservativelogic gates. conservative computing is essentially conditional rerouting ¶3. Rearranging vs. rewriting: Conventional models of computation
are based on rewriting
(e.g., TMs, lambda calculus, register machines, term rewriting systems, signals, C. REVERSIBLE COMPUTING 55 Figure II.11: Alternative notation for Fredkin gate. Post and Markov productions).
But we have seen that overwriting dissipates energy (and is nonconservative).
¶4. In conservative logic we rearrange bits without creating or destroying
them.
(No inﬁnite “bit supply” and no “bit bucket.”)
¶5. Fredkin gate: The Fredkin gate is a conditional swap operation (also
called CSWAP):
(1, a, b) 7! (1, a, b),
(0, a, b) 7! (0, b, a).
The ﬁrst input is a control signal and the other two are data signals.
Here, 0 signals a swap, but some authors use 1 to signal a swap.
See Fig. II.10 and Fig. II.13. Fig. II.11 shows an alternative notation
for the Fredkin gate.
¶6. Note that it is reversible and conservative.
¶7. Universal: The Fredkin gate is a universal Boolean primitive for conservative logic. C.5 Conservative logic circuits ¶1. “A conservativelogic circuit is a directed graph whose nodes are conservativelogic gates and whose arcs are wires of any length [Fig. II.12].” 56 CHAPTER II. PHYSICS OF COMPUTATION A conservativelogic circuit is a directed graph whose nodes are conservativelogic gates and whose arcs are
wires of any length (cf. Figure 3). 3. COMPUTATION IN CONSERVATIVELOGIC CIRCUITS; CONSTANTS
AND GARBAGE
In Figure 4a we have expressed the output variables of the Fredkin gate as explicit functions of the input
variables. The overall functional relationship between input and output is, as we have seen, invertible. On
Figure that closed and (b) open computing are often noninvertible. Thus, special
the other hand, the functions3. (a)one is interested in conservativelogic circuits.
provisionsFigure II.12: in the closed the Fredkin gate conservativelogic of any invertible function that is...
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 Fall '13
 BruceMacLennan
 Logic gate, fredkin gate, Fredkin

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