We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of “back forcing” as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

中文翻译：

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逻辑电路从零强制开始。

我们基于图上的零强迫的概念设计逻辑电路；电路的每个门都是在其中执行零强制的小工具。我们证明了这样的电路可以评估每个单调布尔函数。通过使用两个顶点对每个逻辑位进行编码，我们获得了通用计算。我们还强调了“反向强制”现象，将其作为每个函数的属性。当已经在给定时间步长使用的门的输入被在随后阶段实际执行的计算进一步修改时，在电路中会发生这种现象。最后，我们证明了零强迫也可以用于实现可逆计算。此处介绍的模型为布尔函数的分析提供了潜在的新工具，尤其要注意单调性。而且，鉴于零强迫在量子力学中的应用，与布尔函数的联系可能为量子控制理论和工程量子自旋系统的研究提供新的方向。验证迫零和接触电路计算之间是否存在联系是一个开放的技术问题。