How Can We Construct Reversible Turing Machines in a Very Simple Reversible Cellular Automaton?

A reversible cellular automaton (RCA) is an abstract spatiotemporal model of a reversible world. Using the framework of an RCA, we study the problem of how we can elegantly compose reversible computers from simple reversible microscopic operations. The CA model used here is an elementary triangular partitioned CA (ETPCA), whose spatial configurations evolve according to an extremely simple local transition function. We focus on the particular reversible ETPCA No. 0347, where 0347 is an ID number in the class of 256 ETPCAs. Based on our past studies, we explain that reversible Turing machines (RTMs) can be constructed in a systematic and hierarchical manner in this cellular space. Though ETPCA 0347 is an artificial CA model, this method gives a new vista to find a pathway from a reversible microscopic law to reversible computers. In particular, we shall see that RTMs can be easily realized in a unique method by using a reversible logic element with memory (RLEM) in the intermediate step of the pathway.