Unformatted text preview: tion of information is bounded: No
action at a distance.
¶3. P2. The amount of information which can be encoded in the
state of a ﬁnite system is bounded: This is a consequence of
thermodynamics and quantum theory.
¶4. P3. It is possible to construct macroscopic, dissipative physical devices which perform in a recognizable and reliable way
the logical functions AND, NOT, and FANOUT: This is an
empirical fact. C. REVERSIBLE COMPUTING
C.2.b 53 Conservative logic ¶1. “Computation is based on the storage, transmission, and processing of
discrete signals.”
¶2. Only macroscopic systems are irreversible, so as we go to the microscopic level, we need to understand reversible logic. This leads to new
physical principles.
¶3. P4. Identity of transmission and storage: In a relativistic sense,
they are identical.
¶4. P5. Reversibility: Because microscopic physics is reversible.
¶5. P6. Onetoone composition: Physically, fanout is not trivial, so
we cannot assume that one function output can be substituted for any
number of input variables.
We have to treat fanout as a speciﬁc signalprocessing element.
¶6. P7. Conservation of additive quantities: It can be shown that
in a reversible systems there are a number of independent conserved
quantities.
¶7. In many systems they are additive over the subsystems.
¶8. P8. The topology of spacetime is locally Euclidean: “Intuitively, the amount of ‘room’ available as one moves away from a certain
point in space increases as a power (rather than as an exponential) of
the distance from that point, thus severely limiting the connectivity of
a circuit.”
¶9. What are su cient primitives for conservative computation?
The unit wire and the Fredkin gate. C.3 Unit wire ¶1. Information storage in one reference frame may be information transmission in another.
E.g., leaving a note on a table in an airplane (at rest with respect to
earth or not, or to sun, etc.). (and at its output at an analogous called the state ofathe wiresignalprocessing primitive, namely, the Fredkin
conservative logic, time t + 1) is role is played by si...
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 Fall '13
 BruceMacLennan
 Logic gate, fredkin gate, Fredkin

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