Regular Algebras


Title: Regular Algebras
Authors: Simon Foster and Georg Struth
Submission date: 2014-05-21
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.
  author  = {Simon Foster and Georg Struth},
  title   = {Regular Algebras},
  journal = {Archive of Formal Proofs},
  month   = may,
  year    = 2014,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Kleene_Algebra