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Modularizing the Elimination of r=0 in Kleene Algebra

Christopher Hardin
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Abstract

Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of elimination of hypotheses , which is useful because the equational theory of Kleene algebra is decidable while the universal Horn theory is not. We show that hypotheses of the form r = 0 can still be eliminated in the presence of other hypotheses. This lets us extend any technique for eliminating hypotheses to include hypotheses of the form r = 0.

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Christopher Hardin. 2005-11-28. Modularizing the Elimination of r=0 in Kleene Algebra. https://doi.org/10.2168/lmcs-1(3:4)2005

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