Computational Hierarchy of Elementary Cellular Automata
This work addresses the challenge of evaluating parallel computational systems like cellular automata, offering a method to design Turing-complete and efficient systems, though it is incremental in extending existing complexity measures.
The paper tackled the problem of measuring cellular automata complexity by defining a set of computational tasks based on automata emulation, and found that certain chaotic automata cannot emulate others non-trivially, with results presented as a graph for elementary cellular automata.
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph showing which elementary cellular automata can be emulated by which and show that certain chaotic automata are the only ones that cannot emulate any automata non-trivially. Finally, we use the emulation notion to suggest a novel definition of chaos that we believe is suitable for discrete computational systems. We believe our work can help design parallel computational systems that are Turing-complete and also computationally efficient.