Algebraic structures of directed acyclic graphs: application to concurrent calculus

Abstract

The paper defines an algebraic tool for manipulating directed acyclic graphs (on short dags). The approach we propose combines two mathematical tools—category theory and universal algebra—and it allows an unitary treating of dags transformations. We show that the specification, implementation and programming of concurrent systems can be achieved by using this theory.

Keywords:

• 2W-algebra
• algebraic specification of graphs
• concurrent programming
• graph rewriting

Keywords:

• c.R. categories
• D.3.3
• D.1.3.