Three-rules set of one dimensional cellular automata with two states and three neighbors improves description ability

Abstract

In the present paper, we investigate the description ability of digital sound data by the rule set of one dimensional cellular automata with two state and three neighbors referred to as 1-2-3 CA hereafter. It has been shown that the two-rules set of (#90, #180) has the highest description ability of all the possible two-rules sets. For several sound data, however, the data amount of the resultant codes becomes larger than original data, originating into the limitations of the two-rules set of (#90, #180). In order to overcome the limitations, we try to improve the description ability of digital sound data by adding another rule to (#90, #180). Therefore, we evaluate the description ability for the all the possible sets, where we add another rule to (#90, #180). From computer experiments, for the three-rules set of (#45, #90, #180), the averaged length of the rule sequences of the resultant codes becomes shorter, and a ratio of the reduced search number takes larger for all the data. Thus, we succeed to improve the description ability.