### 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.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Stone_Kleene_Relation_Algebras

- Iterings
- Kleene_Algebras
- Kleene_Relation_Algebras
- Kleene_Relation_Subalgebras
- Matrix_Kleene_Algebras

### Depends on

- Stone Relation Algebras

### Used by

- Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations
- Relational Forests
- Aggregation Algebras

### Auto-related entries

- Kleene Algebra

## Cite

×

Stone_Kleene_Relation_Algebras-AFP

    @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{https://isa-afp.org/entries/Stone_Kleene_Relation_Algebras.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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