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Network Rewriting I: The Foundation
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. (Mathematics/Applied Mathematics)ORCID-id: 0000-0001-6140-180X
2012 (engelsk)Rapport (Annet vitenskapelig)
Abstract [en]

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and Permutations category'), and conversely that the PROP axioms are implicit in the concept of evaluating a network. Ordinary terms and operads constitute the special case that the graph underlying the network is a rooted tree. Furthermore a rewriting theory for networks is developed. Included in this is a subexpression concept for which is given both algebraic and effective graph-theoretical characterisations, a construction of reduction maps from rewriting systems, and an analysis of the obstructions to confluence that can occur. Several Diamond Lemmas for this rewriting theory are given. In addition there is much supporting material on various related subjects. In particular there is a "toolbox" for the construction of custom orders on the free PROP, so that an order can be tailored to suit a specific rewriting system. Other subjects treated are the abstract index notation in a general PROP context and the use of feedbacks (sometimes called traces) in PROPs.

sted, utgiver, år, opplag, sider
2012.
Emneord [en]
Mathematics - Rings and Algebras, 16S15 (Primary) 18D10, 06F25, 15A69 (Secondary), F.4.2
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-20964OAI: oai:DiVA.org:mdh-20964DiVA, id: diva2:642077
Merknad

Accession Number: 1204.2421; DocumentType: working paper; Archive Set: Mathematics; Last Revision Date: 20120411

Tilgjengelig fra: 2013-08-20 Laget: 2013-08-20 Sist oppdatert: 2013-12-31bibliografisk kontrollert

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http://arxiv.org/abs/1204.2421

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