Breaking of the Trade-Off Principle between Computational Universality and Efficiency by Asynchronous Updating

Although natural and bioinspired computing has developed significantly, the relationship between the computational universality and efficiency beyond the Turing machine has not been studied in detail. Here, we investigate how asynchronous updating can contribute to the universal and efficient computation in cellular automata (CA). First, we define the computational universality and efficiency in CA and show that there is a trade-off relation between the universality and efficiency in CA implemented in synchronous updating. Second, we introduce asynchronous updating in CA and show that asynchronous updating can break the trade-off found in synchronous updating. Our finding spells out the significance of asynchronous updating or the timing of computation in robust and efficient computation.