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On the Complexity of Reasoning in Kleene Algebra

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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\imps=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, \begin{itemize} \item if E contains only commutativity assumptions pq=qp, the problem is Π10-complete; \item if E contains only monoid equations, the problem is Π20-complete; \item for arbitrary equations E, the problem is Π11-complete. \end{itemize} The last problem is the universal Horn theory of the *-continuous Kleene algebras. This resolves an open question of Kozen (1994).

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1997-03

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR97-1624

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technical report

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