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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S.: Temperley-Lieb algebra: from knot theory to logic and computation via quantum mechanics. In: Mathematics of Quantum Computing and Technology, pp. 515–558 (2007)
Fiore, M., Leinster, T.: An abstract characterization of Thompson’s group F. Semigroup Forum 80, 325–340 (2010)
Jay, C.B.: Languages for monoidal categories. Journal of Pure and Applied Algebra 59, 61–85 (1989)
Lack, S.: Composing PROPs. Theory and Applications of Categories 13(9), 147–163 (2004)
Mac Lane, S.: Categorical algebra. Bulletin of the American Mathematical Society 71(1), 40–106 (1965)
Milner, R.: Axioms for bigraphical structure. Mathematical Structures in Computer Science 15(6), 1005–1032 (2005)
Milner, R.: The Space and Motion of Communicating Agents. Cambridge University Press (2009)
Pirashvili, T.: On the PROP corresponding to bialgebras. Cahiers de Topologie et Géométrie Différentielle Catégoriques 43(3), 221–239 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fiore, M., Devesas Campos, M. (2013). The Algebra of Directed Acyclic Graphs. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-38164-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38163-8
Online ISBN: 978-3-642-38164-5
eBook Packages: Computer ScienceComputer Science (R0)