2021/05/10 by Jonathan Gorard, Gorard, Jonathan, Manojna Namuduri +3 · 1 citation
Computer Science · Decision Sciences · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Scientific Computing and Data Management #Software Engineering Research
paper · pdf · doi:10.48550/arxiv.2105.04057
openalex publication_date 2021/05/10 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
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.