How can we construct reversible machines out of reversible logic element with memory?

Abstract

Reversible computing is a paradigm of computation closely related to physical reversibility. In this survey/tutorial paper, we discuss topics on reversible logic elements with memory (RLEM), which are used to build reversible computing machines. It is known that any reversible sequential machine (RSM) can be constructed systematically and simply from a rotary element (RE), a typical 2-state RLEM. It is also known that “all” non-degenerate 2-state RLEMs except only four are universal.Thus, RSMs can be built by any one of universal RLEMs. However, so far, no concise construction method has been given except the method of using RE. Here, we show a new simple method of composing RSMs from 2-state RLEMs of ID numbers 4-31 and 3-7.