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

Fast Automated Reasoning over String Diagrams using Multiway Causal Structure