662 research outputs found
Reversible boolean networks II: Phase transition, oscillation, and local structures
We continue our consideration of a class of models describing the reversible
dynamics of Boolean variables, each with inputs. We investigate in
detail the behavior of the Hamming distance as well as of the distribution of
orbit lengths as and are varied. We present numerical evidence for a
phase transition in the behavior of the Hamming distance at a critical value
and also an analytic theory that yields the exact bounds on
We also discuss the large oscillations that we observe in the Hamming
distance for as a function of time as well as in the distribution of
cycle lengths as a function of cycle length for moderate both greater than
and less than . We propose that local structures, or subsets of spins
whose dynamics are not fully coupled to the other spins in the system, play a
crucial role in generating these oscillations. The simplest of these structures
are linear chains, called linkages, and rings, called circuits. We discuss the
properties of the linkages in some detail, and sketch the properties of
circuits. We argue that the observed oscillation phenomena can be largely
understood in terms of these local structures.Comment: 31 pages, 15 figures, 2 table
Techniques for the Synthesis of Reversible Toffoli Networks
This paper presents novel techniques for the synthesis of reversible networks
of Toffoli gates, as well as improvements to previous methods. Gate count and
technology oriented cost metrics are used. Our synthesis techniques are
independent of the cost metrics. Two new iterative synthesis procedure
employing Reed-Muller spectra are introduced and shown to complement earlier
synthesis approaches. The template simplification suggested in earlier work is
enhanced through introduction of a faster and more efficient template
application algorithm, updated (shorter) classification of the templates, and
presentation of the new templates of sizes 7 and 9. A novel ``resynthesis''
approach is introduced wherein a sequence of gates is chosen from a network,
and the reversible specification it realizes is resynthesized as an independent
problem in hopes of reducing the network cost. Empirical results are presented
to show that the methods are effective both in terms of the realization of all
3x3 reversible functions and larger reversible benchmark specifications.Comment: 20 pages, 5 figure
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