A Simple Universal Logic Element and Cellular Automata for Reversible Computing

Reversible computing is a paradigm of computation that reflects physical reversibility, and is considered to be important when designing a logical devices based on microscopic physical law in the near future. In this paper, we focus on a problem how universal computers can be built from primitive elements with very simple reversible rules. We introduce a new reversible logic element called a "rotary element", and show that any reversible Turing machine can be realized as a circuit composed only of them. Such reversible circuits work in a very different fashion from conventional ones. We also discuss a simple reversible cellular automaton in which a rotary element can be implemented.