Rewriting Structured Cospans
arXiv:2001.09029v3 Announce Type: replace-cross Abstract: We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is adhesive or a topos. These results guarantee that double pushout rewriting can be applied in this setting. We then define structured cospan grammars and construct their associated languages via a 2-categorical framework, capturing both network composition and rewrite dynamics. As an application, we show that for graphs, hypergraphs, Petri nets, and their typed variants, any grammar induces the same language as its corresponding discrete grammar. This equivalence enables an inductive characterization
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Abstract:We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is adhesive or a topos. These results guarantee that double pushout rewriting can be applied in this setting. We then define structured cospan grammars and construct their associated languages via a 2-categorical framework, capturing both network composition and rewrite dynamics. As an application, we show that for graphs, hypergraphs, Petri nets, and their typed variants, any grammar induces the same language as its corresponding discrete grammar. This equivalence enables an inductive characterization of rewriting, thereby generalizing classical results from graph transformation to a broader class of categorical models.
Comments: Version accepted by MSCS
Subjects:
Category Theory (math.CT); Formal Languages and Automata Theory (cs.FL); Social and Information Networks (cs.SI)
MSC classes: 18B10
Cite as: arXiv:2001.09029 [math.CT]
(or arXiv:2001.09029v3 [math.CT] for this version)
https://doi.org/10.48550/arXiv.2001.09029
arXiv-issued DOI via DataCite
Submission history
From: Daniel Cicala [view email] [v1] Fri, 24 Jan 2020 14:26:24 UTC (37 KB) [v2] Thu, 29 May 2025 20:53:31 UTC (35 KB) [v3] Thu, 2 Apr 2026 18:33:31 UTC (27 KB)
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