We improve previous results obtained for networks of evolutionary processors — using the operations insertion, deletion, and substitution on strings — with elementary polarizations [Formula: see text] by showing that only seven processors are needed to obtain computational completeness. In the case of not requiring a special output node, only five processors are shown to be sufficient. We also prove that if the communication structure is allowed to be a directed graph without self-loops, then two polarizations are sufficient (with 12 or 17 nodes, depending on the definition). Moreover, we consider the case of not restricting the number of polarizations, thus obtaining the minimal number of three nodes for hybrid systems and even only one node where all three operations can be carried out.

中文翻译：

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具有极化和少量处理器的进化处理器网络的变体

我们改进了先前为进化处理器网络获得的结果——使用字符串上的插入、删除和替换操作——使用基本极化[公式：见文本]，表明只需要七个处理器即可获得计算完整性。在不需要特殊输出节点的情况下，仅五个处理器就足够了。我们还证明，如果允许通信结构是没有自环的有向图，那么两个极化就足够了（有 12 个或 17 个节点，取决于定义）。此外，我们考虑不限制极化数量的情况，从而获得混合系统的最小数量的三个节点，甚至只有一个节点可以执行所有三个操作。