6 research outputs found

    Modularizing the Elimination of r=0 in Kleene Algebra

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    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

    On Tools for Completeness of Kleene Algebra with Hypotheses

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    In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance in NetKAT. Many of these variants fit within the unifying perspective offered by Kleene algebra with hypotheses, which comes with a canonical language model constructed from a given set of hypotheses. For the case of KAT, this model corresponds to the familiar interpretation of expressions as languages of guarded strings. A relevant question therefore is whether Kleene algebra together with a given set of hypotheses is complete with respect to its canonical language model. In this paper, we revisit, combine and extend existing results on this question to obtain tools for proving completeness in a modular way. We showcase these tools by giving new and modular proofs of completeness for KAT, KAO and NetKAT, and we prove completeness for new variants of KAT: KAT extended with a constant for the full relation, KAT extended with a converse operation, and a version of KAT where the collection of tests only forms a distributive lattice

    Modularizing the Elimination of r=0 in Kleene Algebra

    No full text
    Given a universal Horn formula of Kleene algebra with hypotheses of the formr = 0, it is already known that we can efficiently construct an equation whichis valid if and only if the Horn formula is valid. This is an example ofelimination of hypotheses, which is useful because the equational theoryof Kleene algebra is decidable while the universal Horn theory is not. We showthat hypotheses of the form r = 0 can still be eliminated in the presence ofother hypotheses. This lets us extend any technique for eliminating hypothesesto include hypotheses of the form r = 0

    Modularizing the Elimination of r=0 in Kleene Algebra

    No full text
    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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