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We introduce a new model of cellular automaton called a one-dimensional number-conserving partitioned cellular automaton (NC-PCA). An NC-PCA is a system such that a state of a cell is represented by a triple of non-negative integers, and the total (i.e., sum) of integers over the configuration is conserved throughout its evolving (computing) process. It can be thought as a kind of modelization of the physical conservation law of mass (particles) or energy. We also define a reversible version of...
We introduce a new model of cellular automaton called a
one-dimensional number-conserving partitioned cellular automaton (NC-PCA).
An NC-PCA is a system such that a state of a cell is represented by a
triple of non-negative integers, and the total (, sum) of integers over
the configuration is conserved throughout its evolving (computing) process.
It can be thought as a kind of modelization of the physical conservation
law of mass (particles) or energy.
We also define a reversible version...
We define a kind of cellular automaton called a hexagonal partitioned
cellular automaton (HPCA), and study logical universality of
a reversible HPCA.
We give a specific 64-state reversible HPCA
, and
show that a Fredkin gate can be embedded in this cellular space.
Since a Fredkin gate is known to be a universal logic element,
logical universality of
is concluded.
Although the number of states of
is greater than those
of the previous models...
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