Gellular automata are cellular automata with the properties of asynchrony, Boolean totality and noncamouflage. In distributed computing, it is essential to determine whether problems can be solved by self-stable gellular automata. From any initial configuration, self-stable gellular automata converge to desired configurations, as self-stability implies the ability to recover from temporary malfunctions in transitions or states. This paper shows that three typical problems in distributed computing, namely, solving a maze, distance-2 coloring and spanning tree construction, can be solved with self-stable gellular automata.

Gellular automata are cellular automata with the properties of asynchrony, Boolean totality, and non-camouflage. In distributed computing, it is essential to determine whether problems can be solved by self-stable gellular automata. From any initial configuration, self-stable gellular automata converge to desired configurations, as self-stability implies the ability to recover from temporary malfunctions in transitions or states. In this paper, we show that three typical problems in distributed computing, namely, solving a maze, distance-2 coloring, and spanning tree construction, can be solved with self-stable gellular automata.

We summarize our work on gellular automata, which are cellular automata we intend to implement with gel materials. If cellular automata are implemented as materials, it will become possible to realize smart materials with abilities such as self-organization, pattern formation, and self-repair. Furthermore, it may be possible to make a material that can detect the environment and adapt to it. In this article, we present three models of gellular automata, among which the first two have been proposed previously and the third one is proposed here for the first time. Before presenting the models, we briefly discuss why cellular automata are a research target in DNA computing, a field which aims to extract computational power from DNA molecules. Then, we briefly describe the first model. It is based on gel walls with holes that can open and exchange the solutions that surround them. The second model is also based on gel walls but differs in that the walls allow small molecules to diffuse. In presenting the second model, we focus on self-stability, which is an important property of distributed systems, related to the ability to self-repair. Finally, we report our recent attempt, in the third model, to design gellular automata that learn Boolean circuits from input–output sets, i.e., examples of input signals and their expected output signals.