Fungal automata are a nature-inspired computational model, where a rule is alternatively applied verticaly and horizontaly. In this work we study the computational complexity of predicting the dynamics of all fungal freezing totalistic one-dimentional rules of radius $1$, exhibiting various behaviors. Despite efficiently predictable in most cases (with non-deterministic logspace algorithms), a non-linear rule is left open to characterize. We further explore the freezing majority rule (which is totalistic), and prove that at radius $1.5$ it becomes $\mathbf{P}$-complete to predict.

翻译：真菌自动机是一种受自然启发的计算模型，其中规则交替地在垂直和水平方向上应用。本文研究了所有半径为$1$的真菌冻结全同型一维规则动态预测的计算复杂性，这些规则展现出多种行为。尽管在大多数情况下（通过非确定性对数空间算法）可高效预测，但一个非线性规则仍有待进一步刻画其特性。我们进一步探讨了冻结多数规则（属于全同型规则），并证明在半径为$1.5$时，该规则的预测问题成为$\mathbf{P}$-完全问题。