Stone-Kleene Relation Algebras


Title: Stone-Kleene Relation Algebras
Author: Walter Guttmann
Submission date: 2017-07-06
Abstract: We develop Stone-Kleene relation algebras, which expand Stone relation algebras with a Kleene star operation to describe reachability in weighted graphs. Many properties of the Kleene star arise as a special case of a more general theory of iteration based on Conway semirings extended by simulation axioms. This includes several theorems representing complex program transformations. We formally prove the correctness of Conway's automata-based construction of the Kleene star of a matrix. We prove numerous results useful for reasoning about weighted graphs.
  author  = {Walter Guttmann},
  title   = {Stone-Kleene Relation Algebras},
  journal = {Archive of Formal Proofs},
  month   = jul,
  year    = 2017,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Stone_Relation_Algebras
Used by: Aggregation_Algebras, Relational_Disjoint_Set_Forests
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.