Communications of the ACM
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Kleene Algebra with Tests: Completeness and Decidability
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
ACM Transactions on Computational Logic (TOCL)
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Omega algebra, demonic refinement algebra and commands
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Refinement algebra with operators for enabledness and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
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We first recall the concept of Kleene algebra with domain (KAD) and how demonic operators can be defined in this algebra. We then present a new axiomatisation of demonic algebra with domain (DAD). It has fewer axioms than the one given in our RelMiCS 9 paper and the axioms are introduced in a way that facilitates comparisons with KAD. The goal in defining DAD is to capture the essence of the demonic operators as defined in KAD. However, not all DADs are isomorphic to a KAD with demonic operators. We characterise those that are by solving a conjecture stated in the RelMiCS 9 paper. In addition, we present new facts about the independence of the axioms.