The Algebra of Directed Acyclic Graphs
Marcelo Fiore, Marco Devesas Campos
TL;DR
This paper introduces an algebraic framework for directed acyclic graphs (DAGs), providing a formal mathematical foundation and initial-algebra semantics for DAG structures using symmetric monoidal categories.
Contribution
It presents a novel algebraic presentation and equational theory for DAGs, characterizing their structure through a free PROP with input/output interfaces.
Findings
Provides a symmetric monoidal equational theory for DAGs
Characterizes the free PROP as finite abstract DAGs with interfaces
Establishes an initial-algebra semantics for DAG structures
Abstract
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.
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Taxonomy
TopicsLogic, programming, and type systems · Formal Methods in Verification · Logic, Reasoning, and Knowledge