# 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. BibTeX: @article{Stone_Kleene_Relation_Algebras-AFP, author = {Walter Guttmann}, title = {Stone-Kleene Relation Algebras}, journal = {Archive of Formal Proofs}, month = jul, year = 2017, note = {\url{http://isa-afp.org/entries/Stone_Kleene_Relation_Algebras.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Stone_Relation_Algebras Used by: Aggregation_Algebras