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Title:  On the Complexity of Reasoning in Kleene Algebra 
Authors:  Kozen, Dexter 
Keywords:  computer science technical report 
Issue Date:  Mar1997 
Publisher:  Cornell University 
Citation:  http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR971624 
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 $E\imp s=t$, 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, \begin{itemize} \item if $E$ contains only commutativity assumptions $pq=qp$, the problem is $\Pi_1^0$complete; \item if $E$ contains only monoid equations, the problem is $\Pi_2^0$complete; \item for arbitrary equations $E$, the problem is $\Pi_1^1$complete. \end{itemize} The last problem is the universal Horn theory of the *continuous Kleene algebras. This resolves an open question of Kozen (1994). 
URI:  http://hdl.handle.net/1813/7279 
Appears in Collections:  Computer Science Technical Reports

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