Aggregation Algebras


Title: Aggregation Algebras
Author: Walter Guttmann
Submission date: 2018-09-15
Abstract: We develop algebras for aggregation and minimisation for weight matrices and for edge weights in graphs. We verify the correctness of Prim's and Kruskal's minimum spanning tree algorithms based on these algebras. We also show numerous instances of these algebras based on linearly ordered commutative semigroups.
Change history: [2020-12-09]: moved Hoare logic to HOL-Hoare, moved spanning trees to Relational_Minimum_Spanning_Trees (revision dbb9bfaf4283)
  author  = {Walter Guttmann},
  title   = {Aggregation Algebras},
  journal = {Archive of Formal Proofs},
  month   = sep,
  year    = 2018,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Stone_Kleene_Relation_Algebras
Used by: Relational_Minimum_Spanning_Trees
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.