Modularizing the Elimination of r=0 in Kleene Algebra

Details Modularizing the Elimination of r=0 in Kleene Algebra Modularizing the Elimination of r=0 in Kleene Algebra

2005-11-28

arxiv.org/abs/cs/0511097v3

LMCS 1 (3:4) 2005

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-1(3:4)2005

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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