We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewrites is chosen in accordance with the causal structure of the underlying diagrammatic calculus. The combination of the rewriting structure and the causal structure may be elegantly formulated as a weak 2-category equipped with both total and partial monoidal bifunctors, thus providing a categorical semantics for the full multiway evolution causal graph of a generic Wolfram model hypergraph rewriting system. As an illustrative example, we show how a special case of this algorithm enables highly efficient automated simplification of quantum circuits, as represented in the ZX-calculus.

中文翻译：

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使用多向因果结构的字符串图快速自动推理

我们介绍了一种直观的算法方法，用于在一般的双推（DPO）框架内实现字符串图的自动重写，其中，根据底层图解演算的因果结构选择重写的顺序。重写结构和因果结构的组合可以优雅地表述为同时包含全部和部分单等分双函子的弱2类，从而为通用Wolfram模型超图重写系统的完整多路演化因果图提供了分类语义。作为说明性示例，我们展示了该算法的特殊情况如何实现高效的量子电路自动简化，如ZX微积分所示。