## A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events (1994)

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Venue: | Information and Computation |

Citations: | 188 - 23 self |

### BibTeX

@ARTICLE{Kozen94acompleteness,

author = {Dexter Kozen},

title = {A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events},

journal = {Information and Computation},

year = {1994},

volume = {110},

pages = {366--390}

}

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### Abstract

We give a finitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa 's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 Introduction Kleene algebras are algebraic structures with operators +, \Delta, , 0, and 1 satisfying certain axioms. They arise in various guises in a number of settings: relational algebra [22, 23], semantics and logics of programs [14, 24], automata and formal language theory [18, 19], and the design and analysis of algorithms [1, 21, 12]. An important example of a Kleene algebra is Reg \Sigma , the family of regular sets over a finite alphabet \Sigma. The equational theory of this structure has been called the algebra of regular events. This theory was first studied by Infor. and Comput. 110:2 (May 1994), 366--390. A preliminary version of this paper appeared as [16]. Kleene [13], who posed axiomatization as an open problem. Salomaa [2...