### Abstract

Regular algebras axiomatise the equational theory of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of regular algebras given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these classes, formalise a soundness proof for the smallest class (Salomaa's) and obtain completeness of the largest one (Boffa's) relative to a deep result by Krob. In addition we provide a large collection of regular identities in the general setting of Boffa's axiom. Our regular algebra hierarchy is orthogonal to the Kleene algebra hierarchy in the Archive of Formal Proofs; we have not aimed at an integration for pragmatic reasons.

### License

BSD License

### Topics

- Computer science/Automata and formal languages
- Mathematics/Algebra

### Session Regular_Algebras

- Dioid_Power_Sum
- Regular_Algebras
- Regular_Algebra_Models
- Pratts_Counterexamples
- Regular_Algebra_Variants

### Depends on

- Kleene Algebra

## Cite

×

Regular_Algebras-AFP

    @article{Regular_Algebras-AFP,
      author  = {Simon Foster and Georg Struth},
      title   = {Regular Algebras},
      journal = {Archive of Formal Proofs},
      month   = {May},
      year    = {2014},
      note    = {\url{https://isa-afp.org/entries/Regular_Algebras.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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