Simple reversible triangular cellular automata

Morita Kenichi

We introduce the class of elementary triangular partitioned cellular automata (ETPCAs).
It is one of the simplest subclasses of two-dimensional cellular automata.
Its local transition function is described by only four simple transition rules.
In this presentation, a specific reversible ETPCA with an identification number 0347 (denoted by ETPCA 0347) is investigated.
It shows quite complex behavior, and is particularly interesting in the class of ETPCAs.
In ETPCA 0347, there is a moving pattern called a glider, which can be used as a signal in this cellular space.
There are also several useful patterns by which the moving direction and the phase of the glider are controlled.
Utilizing these operations in a tricky way, we implement a reversible logic element with one-bit memory (RLEM).
Using RLEMs we can construct any reversible Turing machine, a theoretical model of a reversible computer.
By above, we see that even from an extremely simple reversible law, reversible computers can be constructed easily in a systematic manner.

数学 [ 410 ]

英語

[作成日] 2017-11-29

[URI] http://uncomp.uwe.ac.uk/HVM/Program_files/posterKeynotes-HHVM.pdf