## On the Complexity of Reasoning in Kleene Algebra (1997)

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Venue: | Information and Computation |

Citations: | 10 - 5 self |

### BibTeX

@ARTICLE{Kozen97onthe,

author = {Dexter Kozen},

title = {On the Complexity of Reasoning in Kleene Algebra},

journal = {Information and Computation},

year = {1997},

volume = {179},

pages = {152--162}

}

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### Abstract

We study the complexity of reasoning in Kleene algebra and *-continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E ! s = t, where E is a finite set of equations. We obtain various levels of complexity based on the form of the assumptions E. Our main results are: for *- continuous Kleene algebra, ffl if E contains only commutativity assumptions pq = qp, the problem is \Pi 0 1 -complete; ffl if E contains only monoid equations, the problem is \Pi 0 2 -complete; ffl for arbitrary equations E, the problem is \Pi 1 1 - complete. The last problem is the universal Horn theory of the *-continuous Kleene algebras. This resolves an open question of Kozen (1994). 1 Introduction Kleene algebra (KA) is fundamental and ubiquitous in computer science. Since its invention by Kleene in 1956, it has arisen in various forms in program logic and semantics [17, 28], relational algebra [27, 32], aut...