backward and forward both run to need may they ,faster run to
are computers If A Turing machine is fine for reasoning about
computers, but it's not an ideal model for building them. Some
more practical components of reversible logic were introduced in
the 1980s by Edward F. Fredkin and Tommaso Toffoli, who were
then working together at MIT. (Fredkin is now at Carnegie Mellon
University, Toffoli at Boston University.) The components are
logic gates, somewhat like AND and OR gates but designed for
reversibility. In any reversible gate the number of inputs must
equal the number of outputs. Moreover, each possible set of
inputs must yield a distinct set of outputs. If this were not
the case—that is, if two or more input patterns had the same
output—then the reverse action of the gate would be ambiguous.
The devices now known as the Fredkin gate and the Toffoli gate
(see illustration on page 109) both have three inputs and three
outputs; and, as required for reversibility, each input pattern
maps to a unique outpu