We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces. Our development provides an initial-algebra semantics for dag structure.
@article{arxiv.1303.0376,
title = {The Algebra of Directed Acyclic Graphs},
author = {Marcelo Fiore and Marco Devesas Campos},
journal= {arXiv preprint arXiv:1303.0376},
year = {2013}
}