Stone-Kleene Relation Algebras

Walter Guttmann

6 July 2017

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.
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@article{Stone_Kleene_Relation_Algebras-AFP,
  author  = {Walter Guttmann},
  title   = {Stone-Kleene Relation Algebras},
  journal = {Archive of Formal Proofs},
  month   = July,
  year    = 2017,
  note    = {\url{http://isa-afp.org/entries/Stone_Kleene_Relation_Algebras.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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