Reversible and conservative elementary triangular partitioned cellular automata
Morita_conservative_RETPCA.pdf 79.9 MB
Eight-state isotropic triangular partitioned cellular automata (TPCAs) are called elementary TPCAs (ETPCAs). They are extremely simple, since each of their local transition functions is described by only four local rules. Among them, we study computational universality of reversible and conservative ETPCAs. There are nine kinds of such ETPCAs. We show six of them are universal, and three are non-universal. Universality is shown by giving a configuration that simulates a Fredkin gate, a universal reversible gate. Computer simulation results are also given as movies and in the attachment files.
This work was supported by JSPS KAKENHI Grant Number 15K00019
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Graduate School of Engineering