Universality Issues in Reversible Computing Systems and Cellular Automata (Extended Abstract)

Universality Issues in Reversible Computing Systems and Cellular Automata (Extended Abstract)

Universality of Reversible Hexagonal Cellular Automata

We define a hexagonal partitioned cellular automaton (HPCA), and study logical universality of a reversible HPCA. We give a specific 64-state reversible HPCA H1, 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 H1 is concluded. Although the number of states of H1 is greater than those of t...

Logical Universality and Self-Reproduction in Reversible Cellular Automata

A reversible cellular automaton (RCA) is a \backward de-terministic" CA in which every connguration of the cellular space has at most one predecessor. Such reversible systems have a close connection to physical reversibility, and have been known to play an important role in the problem of inevitable power dissipation in computing systems. In this paper, we investigate problems of logical univer...

Computation and Construction Universality of Reversible Cellular Automata

An arbitrary d-dimensional cellular automaton can be constructively embedded in a reversible one having d + 1 dimensions. In particular, there exist computationand construction-universal reversible cellular automata. Thus, we explicitly show a way of implementing nontrivial irreversible processes in a reversible medium. Finally, we derive new results for the bounding problem for configurations,...

Number-Conserving Reversible Cellular Automata and Their Computation-Universality

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 connguration is conserved throughout its evolving (computing) process. It can be thought as a kind of modelization o...